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Journal articles on the topic 'Laplace Adomian Decomposition Method (LADM)'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Abdy, Muhammad, Syafruddin Side, and Reza Arisandi. "Penerapan Metode Dekomposisi Adomian Laplace Dalam Menentukan Solusi Persamaan Panas." Journal of Mathematics, Computations, and Statistics 1, no. 2 (2019): 206. http://dx.doi.org/10.35580/jmathcos.v1i2.9243.

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Abstrak. Artikel ini membahas tentang penerapan Metode Dekomposisi Adomian Laplace (LADM) dalam menentukan solusi persamaan panas. Metode Dekomposisi Adomian Laplace merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier yang mengkombinasikan antara tranformasi Laplace dan metode dekomposisi Adomian. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan PanasAbstract. This study discusses the applic

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2

Shior, M. M., B. C. Agbata, U. Karim, Marcos Salvatierra, D. J. Yahaya, and S. Abraham. "Approximate Solution of Fractional Order of Partial Differential Equations Using Laplace-Adomian Decomposition Method in MATLAB." International Journal of Mathematics and Statistics Studies 12, no. 3 (2024): 61–70. http://dx.doi.org/10.37745/ijmss.13/vol12n36170.

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This article presents the application of the Laplace-Adomian Decomposition Method (LADM) for solving partial differential equations (PDEs) in the context of heat conduction and wave propagation. The LADM combines Laplace transform and Adomian decomposition to approximate solutions to PDEs efficiently in MATLAB. The procedure involves transforming the PDE into simpler differential equations, which are then solved iteratively using the Adomian decomposition method. The advantages of LADM include simplicity, flexibility, and applicability to a wide range of PDEs. We demonstrate the effectiveness

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3

Tsai, P. Y., and C. K. Chen. "A New Algorithm on the Solutions of Forced Convective Heat Transfer in a Semi-Infinite Flat Plate." Journal of Mechanics 27, no. 1 (2011): 63–69. http://dx.doi.org/10.1017/jmech.2011.8.

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ABSTRACTIn this paper, a new algorithm is proposed to solve the velocity and temperature fields in the thermal boundary layer flow over a semi-infinite flat plate. Both the flow and heat transfer solutions are calculated accurately by the Laplace Adomian decomposition method, Padé approximant and the optimal design concept. The Laplace Adomian decomposition method (LADM) is a combination of the numerical Laplace transform algorithm with the Adomian decomposition method (ADM). A hybrid method of the LADM combined with the Padé approximant, named the LADM-Padé approximant technique, is introduce

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M. Bahgat, Mohamed S. "Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 8 (2016): 6530–44. http://dx.doi.org/10.24297/jam.v12i8.5075.

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Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.

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Mohamed, Mohamed Z., Tarig M. Elzaki, Mohamed S. Algolam, Eltaib M. Abd Elmohmoud, and Amjad E. Hamza. "New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations." Journal of Applied Mathematics 2021 (March 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/6662645.

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The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series

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6

Richard, Metomou, and Weidong Zhao. "Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation." Journal of Applied Mathematics 2021 (March 5, 2021): 1–19. http://dx.doi.org/10.1155/2021/6626236.

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The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P L / M · called do

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Agbata, B. C., W. Obeng-Denteh, J. Amoah-Mensah, et al. "Numerical solution of fractional order model of measles disease with double dose vaccination." Dutse Journal of Pure and Applied Sciences 10, no. 3b (2024): 202–17. http://dx.doi.org/10.4314/dujopas.v10i3b.19.

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Measles remains a significant public health concern globally, despite the availability of effective vaccines. In this study, we develop a mathematical model of measles disease that integrates the impact of double dose vaccination and utilize the Laplace Adomian Decomposition Method (LADM) as a numerical approach to obtain solutions for the fractional order differential equations governing the model. The model accounts for the dynamics of susceptible, infected, and vaccinated individuals, considering the transmission dynamics of measles in a population with varying vaccination coverage. LADM, c

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8

Ujlayan, Amit, and Mohit Arya. "Approximate Solution of Riccati Differential Equation via Modified Greens Decomposition Method." Defence Science Journal 70, no. 4 (2020): 419–24. http://dx.doi.org/10.14429/dsj.70.14467.

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Riccati differential equations (RDEs) plays important role in the various fields of defence, physics, engineering, medical science, and mathematics. A new approach to find the numerical solution of a class of RDEs with quadratic nonlinearity is presented in this paper. In the process of solving the pre-mentioned class of RDEs, we used an ordered combination of Green’s function, Adomian’s polynomials, and Pade` approximation. This technique is named as green decomposition method with Pade` approximation (GDMP). Since, the most contemporary definition of Adomian polynomials has been used in GDMP

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9

Appadu, Appanah Rao, and Abey Sherif Kelil. "On Semi-Analytical Solutions for Linearized Dispersive KdV Equations." Mathematics 8, no. 10 (2020): 1769. http://dx.doi.org/10.3390/math8101769.

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The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some semi-analytic methods are applied to solve linearized dispersive KdV equations with homogeneous and inhomogeneous source terms. These methods are the Laplace-Adomian decomposition method (LADM), Homotopy perturbation method (HPM), Bernstein-Laplace-Adomian Method (BALDM), and Reduced Differential Transform Method (RDTM). Three numerical experiment

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10

Senjaya Budiman, Manzo, and Daniel Salim. "A note on Laplace Adomian decomposition method on a linear problem." Hilbert Journal of Mathematical Analysis 2, no. 1 (2024): 026–33. http://dx.doi.org/10.62918/hjma.v2i1.16.

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In last two decades, Laplace Adomian Decomposition Method (LADM) is vastly used to solve non-linear (or even fractional order) differential equations. The method approaches the solution with the partial sums of function series. However, it is not easy to show that the limit of the function series is the exact solution of the problem. In this article, we consider a simple problem such as homogenous second-order linear ordinary differential equation with constant coefficients. We prove analytically that the LADM gives the right exact solution to the considered problem.

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11

Attaullah. "Solving Some Linear and Nonlinear PDEs Using Laplace Adomian Decomposition Method." Journal of Nepal Mathematical Society 1, no. 2 (2018): 9–31. http://dx.doi.org/10.3126/jnms.v1i2.41484.

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In this paper, Laplace Adomian decomposition method (LADM) is applied to solve linear and nonlinear partial differential equations (PDEs). With the help of proposed method, we handle the approximated analytical solutions to some interesting classes of PDEs including nonlinear evolution equations, Cauchy reaction-diffusion equations and the Klien-Gordon equations.

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Noeiaghdam, Samad. "Numerical Approximation of Modiﬁed Non-linear SIR Model of Computer Viruses". Contemporary Mathematics 1, № 1 (2019): 34–48. http://dx.doi.org/10.37256/cm.11201959.34-48.

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In this paper, the non-linear modiﬁed epidemiological model of computer viruses is illustrated. For this aim, two semi-analytical methods, the differential transform method (DTM) and the Laplace-Adomian decomposition method (LADM) are applied. The numerical results are estimated for different values of iterations and compared to the results of the LADM and the homotopy analysis transform method (HATM). Also, graphs of residual errors and phase portraits of approximate solutions for n = 5, 10, 15 are demonstrated. The numerical approximations show the performance of the LADM in comparison to th

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13

bin Selamat, Mat Salim, Nur’atikah binti Khusairi, Nurul Izzaty binti Abdul Gaffar, and Siti Nur Syafiqah binti Syed Huzaini. "The Integral Iterative Method for Approximate Solution of Newell-Whitehead-Segel Equation." Mathematical Sciences and Informatics Journal 3, no. 1 (2022): 1–10. http://dx.doi.org/10.24191/mij.v3i1.13009.

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In this paper, the Newell-Whitehead-Segel (NWS) equation is solved using the integral iterative method (IIM) to determine the accuracy and effectiveness of the method. Comparison of results obtained by IIM with the exact solution and other existing results obtained by other methods such as new iterative method (NIM), Adomian decomposition method (ADM) and Laplace Adomian decomposition method (LADM) revealed the accuracy and effectiveness of the method. The approximation results obtained by IIM is comparable with the others. IIM is reliable and easier in solving the nonlinear problems since thi

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Vanenchii, Peter Ayoo, Collins Emmanue Akpan, and Babuje Ibrahim. "A Quantitative Analysis of the Joint Dynamics of the Interconnected Spread of Cholera and Typhoid Diseases." International Journal of Mathematics and Computer Research 13, no. 05 (2025): 5205–22. https://doi.org/10.5281/zenodo.15481066.

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In this paper, a mathematical model that captures the spread of Cholera and Typhoid is considered. The system of equations was solved using Laplace Adomian Decomposition Method (LADM) and was implemented using MATLAB. The analysis showed that an increase in the burden or cases of Cholera will result to an increase of Typhoid fever and vise-versa indicating that there is a symbiotic nature of the relationship between the typhoid disease and the cholera disease.

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Athmani, Khaled, Abdelmalek Hasseine, Djemoui Laiadi, and Chaker Laiadi. "Analytical solution of the 1-D population balance equation using Laplace transformation and Adomian Decomposition Method." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 3 (2024): e12590. https://doi.org/10.54021/seesv5n3-045.

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The population balance equation (PBE) is a fundamental tool in chemical engineering for modeling particulate processes where particle size distribution significantly impacts product quality and process performance. It finds extensive applications in crystallization, polymerization, granulation, L-L extraction and aerosol dynamics. In this study, we present an analytical technique for solving the one-dimensional population balance equation (PBE). This technique combines Laplace transformation with the Adomian Decomposition Method (LADM), where the Laplace transformation is applied with respect

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Mahmood, Shahid, Rasool Shah, Hassan khan, and Muhammad Arif. "Laplace Adomian Decomposition Method for Multi Dimensional Time Fractional Model of Navier-Stokes Equation." Symmetry 11, no. 2 (2019): 149. http://dx.doi.org/10.3390/sym11020149.

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In this research paper, a hybrid method called Laplace Adomian Decomposition Method (LADM) is used for the analytical solution of the system of time fractional Navier-Stokes equation. The solution of this system can be obtained with the help of Maple software, which provide LADM algorithm for the given problem. Moreover, the results of the proposed method are compared with the exact solution of the problems, which has confirmed, that as the terms of the series increases the approximate solutions are convergent to the exact solution of each problem. The accuracy of the method is examined with h

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17

Atokolo, William, Remigius Okeke Aja, Stephen Ekwueme Aniaku, Ifeanyi Sunday Onah, and Godwin C. E. Mbah. "Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease." International Journal of Mathematics and Mathematical Sciences 2022 (July 12, 2022): 1–24. http://dx.doi.org/10.1155/2022/2297630.

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Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to dete

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18

B.C., Agbata, Odeh J.O., Shior M.M, et al. "Application of Laplace-Adomian Decomposition Method (LADM) to Solving Zika Virus Model with Vector Control." GPH - International Journal of Mathematics 07, no. 03 (2024): 82–107. https://doi.org/10.5281/zenodo.11075051.

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<strong>The emergence and spread of vector-borne diseases pose significant public health challenges worldwide, especially in regions where its primary vector, the<em> Aedes aegypti mosquito</em>, thrives. Zika virus (ZIKV) infection represents a pressing concern due to its potential for severe neurological complications and adverse pregnancy outcomes. Effective control strategies are imperative to mitigate ZIKV transmission and reduce the burden of disease. This study explores the application of the Laplace-Adomian Decomposition Method (LADM) to solve a mathematical model describing the dynami

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Jaradat, Emad K., Omar Alomari, Mohammad Abudayah, and Ala’a M. Al-Faqih. "An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method." Advances in Mathematical Physics 2018 (December 5, 2018): 1–11. http://dx.doi.org/10.1155/2018/6765021.

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The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM a

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Benjamin, Idoko Omede, Israel Michael, Kolawole Mustapha Moshood, Amos Jeremiah, Atokolo William, and Abiodun Oguntolu Festus. "APPROXIMATE SOLUTION TO FRACTIONAL ORDER SOIL TRANSMITTED HELMINTH INFECTION MODEL USING LAPLACE ADOMIAN DECOMPOSITION METHOD." GPH - International Journal of Mathematics 07, no. 04 (2024): 16–40. https://doi.org/10.5281/zenodo.11630908.

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<em>In this study, we proposed a fractional order compartmental model based on the Caputo derivative to describe the dynamics of soil-transmitted helminth infection. We employed the Laplace Adomian Decomposition Method (LADM) to derive series solutions for each equation within the system of non-linear differential equations that comprise the epidemiological model. Our findings indicate that the infinite series generated by LADM converges to the exact solution of the system. We performed numerical simulations of the fractional order compartmental deterministic model using MATLAB to validate the

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21

Doğan, Nurettin. "Numerical Treatment of the Model for HIV Infection of CD4+T Cells by Using Multistep Laplace Adomian Decomposition Method." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/976352.

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A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4+T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method

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ur Rahman, Ghaus, Ahmet Yildirim, Fazal Haq, and Emile F. Doungmo Goufo. "Dynamics of an SAIQR influenza model of fractional order via convex incidence rate." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 04 (2020): 2050033. http://dx.doi.org/10.1142/s1793962320500336.

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Influenza A-virus infection represents a global threat causing seasonal outbreaks and pandemics. Among the global threats creating seasonal outbreak, Influenza “A-virus” infection is a dominating theme nowadays. Using the theory of fractional calculus, this study considers an influenza model for quantitative study via the Laplace Adomian Decomposition Method (LADM). We proceed to explore the role of LADM on the proposed model. The method is described and explained for the proposed model while providing some plots to present the behavior of the disease.

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Ghehsareh, Hadi Roohani, Saeid Abbasbandy, and Babak Soltanalizadeh. "Analytical Solutions of the Slip Magnetohydrodynamic Viscous Flow over a Stretching Sheet by Using the Laplace–Adomian Decomposition Method." Zeitschrift für Naturforschung A 67, no. 5 (2012): 248–54. http://dx.doi.org/10.5560/zna.2012-0010.

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In this research, the Laplace-Adomian decomposition method (LADM) is applied for the analytical and numerical treatment of the nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow under slip condition over a permeable stretching surface. The technique is well applied to approximate the similarity solutions of the problem for some typical values of model parameters. The obtained series solutions by the LADM are combined with the Pad´e approximation to improve the accuracy and enlarge the convergence domain of the obtained results. Through tables and figures, the effic

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Haq, Fazal, Kamal Shah, Ghaus ur Rahman, Yongjin Li, and Muhammad Shahzad. "Computational Analysis of Complex Population Dynamical Model with Arbitrary Order." Complexity 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/8918541.

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This paper considers the approximation of solution for a fractional order biological population model. The fractional derivative is considered in the Caputo sense. By using Laplace Adomian decomposition method (LADM), we construct a base function and provide deformation equation of higher order in a simple equation. The considered scheme gives us a solution in the form of rapidly convergent infinite series. Some examples are used to show the efficiency of the method. The results show that LADM is efficient and accurate for solving such types of nonlinear problems.

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ALI, AMIR, ZAMIN GUL, WAJAHAT ALI KHAN, SAEED AHMAD, and SALMAN ZEB. "INVESTIGATION OF FRACTIONAL ORDER SINE-GORDON EQUATION USING LAPLACE ADOMIAN DECOMPOSITION METHOD." Fractals 29, no. 05 (2021): 2150121. http://dx.doi.org/10.1142/s0218348x21501218.

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We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The derivatives considered herein, are taken in Caputo’s sense. The Laplace transform together with the Adomian decomposition method (LADM) is applied to attain analytical approximation of the aforesaid equation. The sG equation having Caputo derivative is solved in the order of series solutions and the results are confirmed by considering two examples with appropriate initial conditions. The numerical simulations are accomplished to compare with the analytical approximations, where qualitatively better agreeme

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Theinchai, Ratchata, Siriwan Chankan, and Weera Yukunthorn. "Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/5052194.

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We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

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Yindoula, J. B., and G. D. Nganga. "COMPARISON OF LAPLACE-ADOMIAN’S DECOMPOSITION METHOD AND LAPLACE VARIATIONAL ITERATION METHOD IN NONLINEAR BOUSSINESQ EQUATION." Advances in Mathematics: Scientific Journal 12, no. 10 (2023): 921–40. http://dx.doi.org/10.37418/amsj.12.10.5.

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Ali, Amjad, Iyad Suwan, Thabet Abdeljawad, and Abdullah. "Numerical simulation of time partial fractional diffusion model by Laplace transform." AIMS Mathematics 7, no. 2 (2022): 2878–90. http://dx.doi.org/10.3934/math.2022159.

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<abstract><p>In the present work, the authors developed the scheme for time Fractional Partial Diffusion Differential Equation (FPDDE). The considered class of FPDDE describes the flow of fluid from the higher density region to the region of lower density, macroscopically it is associated with the gradient of concentration. FPDDE is used in different branches of science for the modeling and better description of those processes that involve flow of substances. The authors introduced the novel concept of fractional derivatives in term of both time and space independent variables in

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Liberty, Ebiwareme, Pere Kormane Fun-Akpo, and Obiem Odok Edmond. "Simulation of unsteady MHD flow of incompressible fluid between two parallel plates using Laplace-Adomian decomposition method." World Journal of Advanced Research and Reviews 14, no. 3 (2022): 136–45. https://doi.org/10.5281/zenodo.7729317.

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The aim of this study is to numerically obtain the solution to an unsteady incompressible fluid confined between two parallel plates with constant velocity. The nonlinear partial differential equation governing the flow is first converted to a nonlinear ordinary differential equation using similarity transformation and solved using the combination of Laplace transform and Adomian decomposition method (LADM). The model parameters affecting the flow geometry is analysed and presented in tables and graphs. The method produces an accurate, elegant, computable, and approximately convergent solution

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Omame, Andrew, and Fiazud Din Zaman. "Solution of the Modified Timefractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method." Acta Mechanica et Automatica 17, no. 1 (2023): 124–32. http://dx.doi.org/10.2478/ama-2023-0014.

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Abstract In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (

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Engworo, G. P., P. O. Ogunniyi, and S. O. Edeki. "Laplace decomposition method for series solutions of systems of linear partial differential models." Journal of Physics: Conference Series 2199, no. 1 (2022): 012022. http://dx.doi.org/10.1088/1742-6596/2199/1/012022.

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Abstract Most of the real-life problems experienced in the industry these days cannot be expressed as a single differential equation but as a system of differential equations. Such structures of linear partial differential models are considered in this work with the aid of the Laplace Adomian decomposition method (LADM) in terms of solutions. Various examples are taken into consideration. The results are easily obtained, are in good agreement when compared to their exact forms. In addition, the proposed method seems effective and efficient; the solutions are graphically presented.

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Soltanalizadeh, Babak, Hadi Roohani Ghehsareh, Ahmet Yıldırım, and Saeid Abbasbandy. "On the Analytic Solution for a Steady Magnetohydrodynamic Equation." Zeitschrift für Naturforschung A 68, no. 6-7 (2013): 412–20. http://dx.doi.org/10.5560/zna.2013-0014.

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The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate result

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Chen, Cha’o Kuang, Yu-Shen Chang, Chin-Chia Liu, and Bang-Shiuh Chen. "Heat dissipation analysis of continuously-moving plate undergoing thermal processing using Laplace Adomian decomposition method." Engineering Computations 34, no. 7 (2017): 2242–55. http://dx.doi.org/10.1108/ec-04-2017-0150.

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Purpose This paper aims to use the Laplace Adomian decomposition method (LADM) to investigate the effects of thermal convection, thermal conduction, surface emissivity and thermal radiation on the heat dissipated by a continuously moving plate undergoing thermal processing. Design/methodology/approach In performing the analysis, it is assumed that the thermal conductivity and surface emissivity of the plate are both temperature-dependent. The accuracy of the LADM solutions is confirmed by comparing the results obtained for the temperature distribution within the plate with those reported in th

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Liberty Ebiwareme, Fun-Akpo Pere Kormane, and Edmond Obiem Odok. "Simulation of unsteady MHD flow of incompressible fluid between two parallel plates using Laplace-Adomian decomposition method." World Journal of Advanced Research and Reviews 14, no. 3 (2022): 136–45. http://dx.doi.org/10.30574/wjarr.2022.14.3.0456.

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The aim of this study is to numerically obtain the solution to an unsteady incompressible fluid confined between two parallel plates with constant velocity. The nonlinear partial differential equation governing the flow is first converted to a nonlinear ordinary differential equation using similarity transformation and solved using the combination of Laplace transform and Adomian decomposition method (LADM). The model parameters affecting the flow geometry is analysed and presented in tables and graphs. The method produces an accurate, elegant, computable, and approximately convergent solution

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35

Selamat, Mat Salim, and Nurul Syahiera Mohamad Ozman. "Application of the Banach Contraction Method to the Benjamin-Bona Mahony Equation: Comparative Analysis with the Laplace Adomian Decomposition Method." Semarak International Journal of Fundamental and Applied Mathematics 4, no. 1 (2024): 75–84. https://doi.org/10.37934/sijfam.4.1.7584.

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The Benjamin-Bona Mahony (BBM) equation, a nonlinear dispersive wave model, plays a crucial role in fields such as fluid dynamics and plasma physics. Solving the BBM equation analytically is challenging, necessitating numerical and semi-analytical approaches. This study investigates the application of the Banach Contraction Method (BCM) to the BBM equation, comparing its performance with the Laplace Adomian Decomposition Method (LADM). By employing iterative approximations, BCM demonstrates convergence to unique solutions under specific conditions, ensuring reliability. Two examples of the BBM

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Edeki, Sunday O., Tanki Motsepa, Chaudry Masood Khalique, and Grace O. Akinlabi. "The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method." Open Physics 16, no. 1 (2018): 780–85. http://dx.doi.org/10.1515/phys-2018-0097.

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Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions ar

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Jaradat, Emad K., Omar Alomari, Audai A. Al-Zgool, and Omar K. Jaradat. "Semi-Analytical Solutions of the Rayleigh Oscillator Using Laplace–Adomian Decomposition and Homotopy Perturbation Methods: Insights into Symmetric and Asymmetric Dynamics." Symmetry 17, no. 7 (2025): 1081. https://doi.org/10.3390/sym17071081.

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This study investigates the solution structure of the nonlinear Rayleigh oscillator equation through two widely used semi-analytical techniques: the Laplace–Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM). The Rayleigh oscillator exhibits inherent asymmetry in its nonlinear damping term, which disrupts the time-reversal symmetry present in linear oscillatory systems. Applying the LADM and HPM, we derive approximate solutions for the Rayleigh oscillator. Due to the absence of exact analytical solutions in the literature, these approximations are benchmarked agains

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Alsa'di,, K., N. M. A. Nik Long, and Z. K. Eshkuvatov. "Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space." Malaysian Journal of Mathematical Sciences 18, no. 3 (2024): 469–89. http://dx.doi.org/10.47836/mjms.18.3.01.

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This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer's fixed-point theorem, the Banach contraction theorem and the Arzel\`{a}-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman's inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both line

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Abuasbeh, Kinda, Ramsha Shafqat, Ammar Alsinai, and Muath Awadalla. "Analysis of the Mathematical Modelling of COVID-19 by Using Mild Solution with Delay Caputo Operator." Symmetry 15, no. 2 (2023): 286. http://dx.doi.org/10.3390/sym15020286.

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This work investigates a mathematical fractional-order model that depicts the Caputo growth of a new coronavirus (COVID-19). We studied the existence and uniqueness of the linked solution using the fixed point theory method. Using the Laplace Adomian decomposition method (LADM), we explored the precise solution of our model and obtained results that are stated in terms of infinite series. Numerical data were then used to demonstrate the use of the new derivative and the symmetric structure that we created. When compared to the traditional order derivatives, our results under the new hypothesis

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Paul, Susmita, Sankar Prasad Mondal, Paritosh Bhattacharya, and Kripasindhu Chaudhuri. "Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem." International Journal of Differential Equations 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/8921710.

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We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF meth

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Lee, Sen-Yung, Li-Kuo Chou, and Chao Kuang Chen. "Nonlinear temperature and thermal stress analysis of annular fins with time dependent boundary condition." Engineering Computations 35, no. 3 (2018): 1444–59. http://dx.doi.org/10.1108/ec-07-2017-0289.

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PurposeThe purpose of this paper is to propose the Laplace Adomian Decomposition Method (LADM) for studying the nonlinear temperature and thermal stress analysis of annular fins with time-dependent boundary condition.Design/methodology/approachThe nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root is studied by the LADM. The radiation effect is considered. The convective heat transfer coefficient is considered as a temperature function.FindingsThe proposed solution

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Ali, Hegagi Mohamed, Hijaz Ahmad, Sameh Askar, and Ismail Gad Ameen. "Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations." Fractal and Fractional 6, no. 1 (2022): 32. http://dx.doi.org/10.3390/fractalfract6010032.

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In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity

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Ebiwareme, Liberty, Kubugha Wilcox Bunonyo, and Obinna Nwokorie. "An analysis of convergence of hybridized approximation techniques for the analytical solution of partial differential equations." International Research Journal of Pure and Applied Physics 10, no. 1 (2023): 24–58. http://dx.doi.org/10.37745/ijrjpap.13/vol10n12458.

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In this paper, we use the hybridization of two well-known semi-analytical methods to obtain the numerical solutions for some special linear and nonlinear partial differential equations that are predominant in most physical science disciplines. The first among these methods is the coupling of Laplace transform and Adomian decomposition method (LADM) while the second method is standard Homotopy perturbation method with Laplace transform method (HPTM). The accuracy and dependability of these proposed techniques is confirmed by applying them to solve linear and nonlinear Kleidon-Gordon equations,

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Alkahtani, Badr Saad T. "A Fractional-Order Investigation of Vaccinated SARS-CoV-2 Epidemic Model with Caputo Fractional Derivative." Journal of Function Spaces 2022 (March 24, 2022): 1–11. http://dx.doi.org/10.1155/2022/5877970.

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In this paper, we consider a fractional-order mathematical system comprising four different compartments for the recent pandemic of SARS-CoV-2 with regard to global and singular kernels of Caputo fractional operator. The SARS-CoV-2 fractional mathematical model is analyzed for series-type solution by Laplace–Adomian decomposition techniques (LADM) and homotopy perturbation method (HPM). The whole quantity of each compartment is divided into small parts, and then the sum of these all parts is written as a series solution for each agent of the system, while the nonlinear part is decomposed using

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Loyinmi, Adedapo Chris. "Analysis of Two Hybrid Schemes to Solve the Benjamin-Bona-Mahony (BBM) Equation." Kathmandu University Journal of Science, Engineering and Technology 18, no. 1 (2024): 1–15. http://dx.doi.org/10.3126/kuset.v18i1.67498.

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In this research, we compare and contrast two numerical methods, the Laplace Adomian Decomposition Method (LADM) and the Elzaki Projected Differential Transform Method (EPDTM), for solving the Benjamin-Bona-Mahony (BBM) equation, and this helps in evaluating their performance, assessing robustness, gaining insights into solution behavior, validating results, generalizing their applicability, and advancing the field. This rigorous comparisons validates the efficacy of the methods as we compare the exact results and the results of LADM and EPDTM, plotting the convergent of the two methods to ide

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Lichae, Bijan Hasani, Jafar Biazar, and Zainab Ayati. "The Fractional Differential Model of HIV-1 Infection of CD4+T-Cells with Description of the Effect of Antiviral Drug Treatment." Computational and Mathematical Methods in Medicine 2019 (January 8, 2019): 1–12. http://dx.doi.org/10.1155/2019/4059549.

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In this paper, the fractional-order differential model of HIV-1 infection of CD4+T-cells with the effect of drug therapy has been introduced. There are three components: uninfected CD4+T-cells,x, infected CD4+T-cells,y, and density of virions in plasma,z. The aim is to gain numerical solution of this fractional-order HIV-1 model by Laplace Adomian decomposition method (LADM). The solution of the proposed model has been achieved in a series form. Moreover, to illustrate the ability and efficiency of the proposed approach, the solution will be compared with the solutions of some other numerical

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Nawaz, Rashid, Aaqib Iqbal, Hina Bakhtiar, et al. "A New Extension of Optimal Auxiliary Function Method to Fractional Non-Linear Coupled ITO System and Time Fractional Non-Linear KDV System." Axioms 12, no. 9 (2023): 881. http://dx.doi.org/10.3390/axioms12090881.

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In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze fractional non-linear coupled ITO systems and non-linear KDV systems, which feature equations of a fractional order in time. We compare the results obtained for the ITO system with those derived from the Homotopy Perturbation Method (HPM) and the New Iterative Method (NIM), and for the KDV system with the Laplace Adomian Decomposition Method (LADM). OAFM demonstrates rema

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Muhammad Khan, Faiz, Amjad Ali, Abdullah, Kamal Shah, Aziz Khan, and Ibrahim Mahariq. "Analytical Approximation of Brusselator Model via LADM." Mathematical Problems in Engineering 2022 (September 28, 2022): 1–14. http://dx.doi.org/10.1155/2022/8778805.

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In this paper, we have investigated the fractional-order Brusselator model for the approximate analytical solution. The concerned coupled system of nonlinear fractional-order partial differential equations (PDEs) has been considered in many research articles to describe various real-world problems. Nonlinear dynamical systems are increasingly used in autocatalytic chemical reactions. These types of autocatalytic chemical reaction models have a variety of applications in several physical systems. The Brusselator model is one of the intensively used autocatalytic models. We have obtained the app

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Ali, Amir, Abid Ullah Khan, Obaid Algahtani, and Sayed Saifullah. "Semi-analytical and numerical computation of fractal-fractional sine-Gordon equation with non-singular kernels." AIMS Mathematics 7, no. 8 (2022): 14975–90. http://dx.doi.org/10.3934/math.2022820.

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<abstract><p>In this article, we study the nonlinear sine-Gordon equation (sGE) under Mittag-Leffler and exponential decay type kernels in a fractal fractional sense. The Laplace Adomian decomposition method (LADM) is applied to investigate the sGE under the above-mentioned operators. The convergence analysis is provided for the proposed method. The results are validated by considering numerical examples with different initial conditions for both kernels and confirm the competence of the proposed technique. It is revealed that the obtained series solutions of the model with fractal

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Bagyalakshmi, Morachan, and G. SaiSundarakrishnan. "Tarig Projected Differential Transform Method to solve fractional nonlinear partial differential equations." Boletim da Sociedade Paranaense de Matemática 38, no. 3 (2019): 23–46. http://dx.doi.org/10.5269/bspm.v38i3.34432.

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Recent advancement in the field of nonlinear analysis and fractional calculus help to address the rising challenges in the solution of nonlinear fractional partial differential equations. This paper presents a hybrid technique, a combination of Tarig transform and Projected Differential Transform Method (TPDTM) to solve nonlinear fractional partial differential equations. The effectiveness of the method is examined by solving three numerical examples that arise in the field of heat transfer analysis. In this proposed scheme, the solution is obtained as a convergent series and the result is use

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