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Journal articles on the topic 'Adomian Decomposition Method'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

Biazar, Jafar, and Mohsen Didgar. "Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains." International Journal of Differential Equations 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/580741.

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We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.

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2

Abassy, Tamer A. "Improved Adomian decomposition method." Computers & Mathematics with Applications 59, no. 1 (January 2010): 42–54. http://dx.doi.org/10.1016/j.camwa.2009.06.009.

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3

Hosseini, S. Gh, and S. Abbasbandy. "Solution of Lane-Emden Type Equations by Combination of the Spectral Method and Adomian Decomposition Method." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/534754.

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The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obtained result reveals that method is of higher efficiency, validity, and accuracy.

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4

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 (May 19, 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 application of Adomian Laplace Decomposition Method (ALDM) in determining the solution of heat equation. Adomian Laplace Decomposition Method is a semi analytical method to solve nonlinear differential equations that combine Laplace transform and Adomian decomposition method. Based on the calculation result, Adomian Laplace decomposition method can approach the settlement of ordinary nonlinear differential equations.Keywords: Adomian Laplace Decomposition Method, Partial Differential Equation, Heat Equation.

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Shaheed, N. H., and Y. Muhammad. "Adomian Decomposition Tarig Transform Method." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2322/1/012005.

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Abstract Adomian decomposition Tarig transform technique (ADTTM) is a new variant of the A domian decomposition method for solving various models of partial differential equations. The Adomian decomposition method and the Tarig transform are combined in the ADTTM. The research makes extensive use of concrete instances. For many linear and nonlinear models, the new modification provides a useful tool.

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6

BİLDİK, Necdet, and Sinan DENİZ. "MODIFIED ADOMIAN DECOMPOSITION METHOD FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS." Review of the Air Force Academy 13, no. 3 (December 16, 2015): 21–26. http://dx.doi.org/10.19062/1842-9238.2015.13.3.3.

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7

OLAYİWOLA, Morufu Oyedunsi, and Kabiru KAREEM. "A New Decomposition Method for Integro-Differential Equations." Cumhuriyet Science Journal 43, no. 2 (June 29, 2022): 283–88. http://dx.doi.org/10.17776/csj.986019.

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This present study developed a new Modified Adomian Decomposition Method (MADM) for integro-differential equations. The modification was carried out by decomposing the source term function into series. The terms in the series were then selected in pairs to form the initials for the prevailing approximation. The newly modified Adomian decomposition method (MADM) accelerates the convergence of the solution faster than the Standard Adomian Decomposition Method (SADM). This study recommends the use of the MADM for solving integro-differential equations.

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8

Lai, Xian-Jing, Jie-Fang Zhang, and Jian-Fei Luo. "Adomian Decomposition Method for Approximating the Solution of the High-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation." Zeitschrift für Naturforschung A 61, no. 5-6 (June 1, 2006): 205–15. http://dx.doi.org/10.1515/zna-2006-5-601.

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In this paper, the decomposition method is implemented for solving the high-order dispersive cubic-quintic nonlinear Schrödinger equation. By means of Maple the Adomian polynomials of obtained series solution have been calculated. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solutions of nonlinear problems. - PACS numbers: 02.30.Jr; 02.60.Cb; 42.65.Tg

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9

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 double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

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10

El-Sayed El-Danaf, Talaat, Mfida Ali Zaki, and Wedad Moenaaem. "New numerical technique for solving the fractional Huxley equation." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 8 (October 28, 2014): 1736–54. http://dx.doi.org/10.1108/hff-07-2013-0216.

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Purpose – The purpose of this paper is to investigate the possibility of extension to the variational iteration and the Adomian decomposition methods for solving nonlinear Huxley equation with time-fractional derivative. Design/methodology/approach – Objectives achieved the main methods: the fractional derivative of f (x) in the Caputo sense is first stated. Second, the time-fractional Huxley equation is written in a differential operator form where the differential operator is in Caputo sense. After acting on both sides by the inverse operator of the fractional differential operator in Caputo sense, the Adomian's decomposition is then used to get the power series solution of the resulted time-fractional Huxley equation. Also, a second objective is achieved by applying the variational iteration method to get approximate solutions for the time-fractional Huxley equation. Findings – There are some important findings to state and summarize here. First, the variational iteration method and the decomposition method provide the solutions in terms of convergent series with easily computable components for this considered problem. Second, it seems that the approximate solution of time-fractional Huxley equation using the decomposition method converges faster than the approximate solution using the variational iteration method. Third, the variational iteration method handles nonlinear equations without any need for the so-called Adomian polynomials. However, Adomian decomposition method provides the components of the exact solution, where these components should follow the summation given in Equation (21). Originality/value – This paper presents new materials in terms of employing the variational iteration and the Adomian decomposition methods to solve the problem under consideration. It is expected that the results will give some insightful conclusions for the used techniques to handle similar fractional differential equations. This emphasizes the fact that the two methods are applicable to a broad class of nonlinear problems in fractional differential equations.

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11

Kareem, Kabiru Oyeleye, Morufu Olayiwola, Oladapo Asimiyu, Yunus Akeem, Kamilu Adedokun, and Ismail Alaje. "On the Solution of Volterra Integro-differential Equations using a Modified Adomian Decomposition Method." Jambura Journal of Mathematics 5, no. 2 (August 1, 2023): 265–77. http://dx.doi.org/10.34312/jjom.v5i2.19029.

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The Adomian decomposition method’s effectiveness has been demonstrated in recent research, the process requires several iterations and can be time-consuming. By breaking down the source term function into series, the current work introduced a new decomposition approach to the Adomian decomposition method. As compared to the conventional Adomian decomposition approach, the newly devised method hastens the convergence of the solution. Numerical experiments were provided to show the superiority qualities.

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Sanusi, Wahidah, Syafruddin Side, and Beby Fitriani. "Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace." Journal of Mathematics, Computations, and Statistics 2, no. 2 (May 12, 2020): 173. http://dx.doi.org/10.35580/jmathcos.v2i2.12580.

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Abstrak. Penelitian ini mengkaji terbentuknya persamaan Transport dan menerapkan metode Dekomposisi Adomian Laplace dalam menentukan solusi persamaan Transport. Persamaan transport merupakan salah satu bentuk dari persamaan diferensial parsial. Bentuk umum persamaan Transport yaitu: Metode Dekomposisi Adomian Laplace merupakan kombinasi antara dua metode yaitu metode dekomposisi adomian dan transformasi laplace. Penyelesaian persamaan Transport dengan metode Dekomposisi Adomian Laplace dilakukan dengan cara menggunakan tranformasi Laplace, mensubstitusi nilai awal, menyatakan solusi dalam bentuk deret tak hingga dan menggunakan invers transformasi laplace . Metode ini juga merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata Kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan Transport.This research discusses the solving of Transport equation applying Laplace Adomian Decomposition Method. Transport equation is one form of partial differential equations. General form of Transport equation is: Laplace Adomian Decomposition Method that combine between Laplace transform and Adomian Decomposition Method. The steps used to solve Transport equation are applying Laplace transform, initial value substitution, defining a solution as infinite series, then using the inverse Laplace transform. This method is a semi analytical method to solve for nonlinear ordinary differential equation. Based on the calculation results, the Laplace Adomian decomposition method can solve the solution of nonlinear ordinary differential equation.Keywords: Laplace Adomian Decomposition Method, Partial Differential Equation, Transport Equation.

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13

Ahmad, Najmuddin, and Balmukund Singh. "Numerical Solution of Integral Equation by using New Modified Adomian Decomposition Method and Newton Raphson Methods." Regular issue 10, no. 8 (June 30, 2021): 5–11. http://dx.doi.org/10.35940/ijitee.h9069.0610821.

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In this paper, we discuss the numerical solution of Adomian decomposition method and Taylor’s expansion method in Volterra linear integral equation. And we apply modified Adomian decomposition method and Newton Raphson method in Volterra nonlinear integral equation with the help of example and estimated an error in MATLAB 13 versions.

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14

Liu, Zhi Feng, Chun Hua Guo, Li Gang Cai, Wen Tong Yang, and Zhi Min Zhang. "Comparison of Adomian Decomposition Method and Differential Transformation Method for Vibration Problems of Euler-Bernoulli Beam." Applied Mechanics and Materials 157-158 (February 2012): 476–83. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.476.

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In this paper, we compare the Differential transformation method and Adomian decomposition method to solve Euler-Bernoulli Beam vibration problems. The natural frequencies and mode shapes of the clamped-free uniform Euler-Bernoulli equation are calculated using the two methods. The Adomian decomposition method avoids the difficulties and massive computational work inherent in Differential transformation method by determining the very rapidly convergent analytic solutions directly. We found the solution between the two methods to be quite close. According to calculation of eigenvalues, natural frequencies and mode shapes, we compare the convergence of Differential transformation method and Adomian decomposition method. The two methods can be alternative ways to solve linear and nonlinear higher-order initial value problems.

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15

Ma, Zheng-Yi. "The Decomposition Method for Studying a Higher-Order Nonlinear Schrödinger Equation in Atmospheric Dynamics." Zeitschrift für Naturforschung A 62, no. 7-8 (August 1, 2007): 387–95. http://dx.doi.org/10.1515/zna-2007-7-806.

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The Adomian decomposition method is implemented for solving a higher-order nonlinear Schrödinger equation in atmospheric dynamics. By means of Maple, the Adomian polynomials of an obtained series solution have been calculated. The results reported in this paper provide further evidence of the usefulness of Adomian decomposition for obtaining solutions of nonlinear problems.

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SEMINARA, SILVIA, and MARIA INES TROPAREVSKY. "SOME REMARKS ON ADOMIAN DECOMPOSITION METHOD." Poincare Journal of Analysis and Applications 01, no. 02 (December 30, 2014): 63–70. http://dx.doi.org/10.46753/pjaa.2014.v01i02.003.

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17

Lin, Yinwei, Tzon-Tzer Lu, and Cha'o-Kuang Chen. "Adomian Decomposition Method Using Integrating Factor." Communications in Theoretical Physics 60, no. 2 (August 2013): 159–64. http://dx.doi.org/10.1088/0253-6102/60/2/03.

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18

Babolian, E., and A. Davari. "Numerical implementation of Adomian decomposition method." Applied Mathematics and Computation 153, no. 1 (May 2004): 301–5. http://dx.doi.org/10.1016/s0096-3003(03)00646-5.

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19

El-Wakil, S. A., and M. A. Abdou. "New applications of Adomian decomposition method." Chaos, Solitons & Fractals 33, no. 2 (July 2007): 513–22. http://dx.doi.org/10.1016/j.chaos.2005.12.037.

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20

Tien, Wei-Chung, and Cha’o-Kuang Chen. "Adomian decomposition method by Legendre polynomials." Chaos, Solitons & Fractals 39, no. 5 (March 2009): 2093–101. http://dx.doi.org/10.1016/j.chaos.2007.06.066.

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21

Hosseini, M. M. "Adomian decomposition method with Chebyshev polynomials." Applied Mathematics and Computation 175, no. 2 (April 2006): 1685–93. http://dx.doi.org/10.1016/j.amc.2005.09.014.

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22

Chen, Wenhai, and Zhengyi Lu. "An algorithm for Adomian decomposition method." Applied Mathematics and Computation 159, no. 1 (November 2004): 221–35. http://dx.doi.org/10.1016/j.amc.2003.10.037.

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23

Luo, Xing-Guo. "A two-step Adomian decomposition method." Applied Mathematics and Computation 170, no. 1 (November 2005): 570–83. http://dx.doi.org/10.1016/j.amc.2004.12.010.

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Ujlayan, Amit, and Mohit Arya. "Approximate Solution of Riccati Differential Equation via Modified Greens Decomposition Method." Defence Science Journal 70, no. 4 (July 13, 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. Therefore, a specific class of Adomian polynomials is used to advance GDMP to modified green decomposition method with Pade` approximation (MGDMP). Further, MGDMP is applied to solve some special RDEs, belonging to the considered class of RDEs, absolute error of the obtained solution is compared with Adomian decomposition method (ADM) and Laplace decomposition method with Pade` approximation (LADM-Pade`). As well, the impedance of the method emphasised with the comparative error tables of the exact solution and the associated solutions with respect to ADM, LADM-Pade`, and MGDMP. The observation from this comparative study exhibits that MGDMP provides an improved numerical solution in the given interval. In spite of this, generally, some of the particular RDEs (with variable coefficients) cannot be easily solved by some of the existing methods, such as LADM-Pade` or Homotopy perturbation methods. However, under some limitations, MGDMP can be successfully applied to solve such type of RDEs.

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Brinda Sari, Lukita Ambarwati, and Eti Dwi Wiraningsih. "Solusi Semi Analitik Persamaan Burgers Menggunakan Metode Dekomposisi Adomian Laplace." JMT : Jurnal Matematika dan Terapan 5, no. 2 (August 31, 2023): 67–77. http://dx.doi.org/10.21009/jmt.5.2.2.

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Burgers equation is a partial differential equation which has important rule in fluid mechanics. Because it has nonlinear terms, the exact solution is complicated to find. Therefore many methods have been developed to find the approximate solution that can estimate the exact solution. In this research, the Laplace Adomian decomposition method is applied to calculate the approximate solution of Burgers equation. The method is a semi-analytical method to resolve nonlinear differential equation. By the numerical simulation, we obtained a result that the approximate solution by this method can estimate the exact solution with the sum of absolute and relative error less than those using approximate solution obtained by the Adomian decomposition method without the use of Laplace transform. Therefore the Laplace Adomian decomposition method is more accurate than the Adomian decomposition method in order to estimate the exact solution of the Burgers equation.

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Hajmohammadi, Mohammad Reza, Seyed Salman Nourazar, and Ali Habibi Manesh. "Semi-analytical treatments of conjugate heat transfer." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 3 (October 5, 2012): 492–503. http://dx.doi.org/10.1177/0954406212463514.

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A new algorithm is proposed based on semi-analytical methods to solve the conjugate heat transfer problems. In this respect, a problem of conjugate forced-convective flow over a heat-conducting plate is modeled and the integro-differential equation occurring in the problem is solved by two lately-proposed approaches, Adomian decomposition method and differential transform method. The solution of the governing integro-differential equation for temperature distribution of the plate is handled more easily and accurately by implementing Adomian decomposition method/differential transform method rather than other traditional methods such as perturbation method. A numerical approach is also performed via finite volume method to examine the validity of the results for temperature distribution of the plate obtained by Adomian decomposition method/differential transform method. It is shown that the expressions for the temperature distribution in the plate obtained from the two methods, Adomian decomposition method and differential transform method, are the same and show closer agreement to the results calculated from numerical work in comparison with the expression obtained by perturbation method existed in the literature.

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Khan, Hassan, Rasool Shah, Poom Kumam, Dumitru Baleanu, and Muhammad Arif. "An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations." Mathematics 7, no. 5 (May 13, 2019): 426. http://dx.doi.org/10.3390/math7050426.

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In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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Turkyilmazoglu, Mustafa. "A reliable convergent Adomian decomposition method for heat transfer through extended surfaces." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 11 (November 5, 2018): 2551–66. http://dx.doi.org/10.1108/hff-01-2018-0003.

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PurposeThis paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the heat transfer enhancement phenomenon. It is modified to include a parameter adjusting and controlling the convergence of the resulting Adomian series.Design/methodology/approachIt is shown that without such a convergence control parameter, some of the published data in the literature concerning the problem are lacking accuracy or the worst is untrustful. With the proposed amendment over the classical Adomian decomposition method, it is easy to gain the range of parameters guaranteeing the convergence of the Adomian series.FindingsWith the presented improvement, the reliable behavior of the fin tip temperature and the fin efficiency of the most interested from practical perspective are easily predicted.Originality/valueThe relevant future studies involving the fin problems covering many physical nonlinear properties must be properly treated as guided in this paper, while the Adomian decomposition method is adopted for the solution procedure.

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Kim, Weonbae, and Changbum Chun. "A Modified Adomian Decomposition Method for Solving Higher-Order Singular Boundary Value Problems." Zeitschrift für Naturforschung A 65, no. 12 (December 1, 2010): 1093–100. http://dx.doi.org/10.1515/zna-2010-1213.

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In this paper, we present a reliable modification of the Adomian decomposition method for solving higher-order singular boundary value problems. He’s polynomials are also used to overcome the complex and difficult calculation of Adomian polynomials occurring in the application of the Adomian decomposition method. Numerical examples are given to illustrate the accuracy and efficiency of the presented method, revealing its reliability and applicability in handling the problems with singular nature.

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Manaa, Saad A., and Nergiz M. Mosa. "Adomian Decomposition and Successive Approximation Methods for Solving Kaup-Boussinesq System." Science Journal of University of Zakho 7, no. 3 (September 30, 2019): 101–7. http://dx.doi.org/10.25271/sjuoz.2019.7.3.582.

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The Kaup-Boussinesq system has been solved numerically by using two methods, Successive approximation method (SAM) and Adomian decomposition method (ADM). Comparison between the two methods has been made and both can solve this kind of problems, also both methods are accurate and has faster convergence. The comparison showed that the Adomian decomposition method much more accurate than Successive approximation method.

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Abdy, Muhammad, Maya Sari Wahyuni, and Narisa Fahira Awaliyah. "Solusi Persamaan Adveksi-Difusi dengan Metode Dekomposisi Adomian Laplace." Journal of Mathematics Computations and Statistics 5, no. 1 (May 1, 2022): 40. http://dx.doi.org/10.35580/jmathcos.v5i1.32249.

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Artikel ini membahas tentang solusi dari persamaan adveksi-difusi. Persamaan adveksi-difusi merupakan persamaan matematis yang didesain untuk mempelajari fenomena transpor polutan. Pada artikel ini, metode yang digunakan untuk menentukan solusi persamaan adveksi-difusi yaitu metode dekomposisi Adomian-Laplace. Metode dekomposisi Adomian Laplace adalah salah satu metode yang dapat digunakan untuk menyelesaikan persamaan diferensial yang mengkombinasikan metode transformasi Laplace dan metode dekomposisi Adomian. Solusi persamaan adveksi-difusi diperoleh dengan menerapkan tranformasi laplace pada persamaan adveksi-difusi, mensubtitusi syarat awal, menyatakan solusi dalam bentuk deret tak hingga, menentukan suku-sukunya, dan menerapkan invers transformasi Laplace pada suku-suku dari deret tak hingga tersebut. Hasil dari tulisan ini adalah solusi persamaan adveksi-difusi dapat diperoleh dengan metode dekomposisi Adomian Laplace.Kata Kunci: Persamaan Diferensial, Persamaan Adveksi-Difusi, Metode Dekomposisi Adomian Laplace.This paper discusses about the solution of advection-diffusion equation. The advection-diffusion equation is a mathematical equation designed to study the phenomenon of pollutant transport. This paper is using Laplace Adomian Decomposition method to solve the advection-diffusion equation. The Laplace Adomian decomposition method is one of method which can be used to solve a differential equation that combines Laplace transform method and Adomian decomposition method. The solution is obtained by applying the Laplace transform to the advection-diffusion equation, substituting the initial conditions, converting the solution into the form of an infinite series, determining the terms, and applying the inverse Laplace transform to the terms of the infinite series. The results of this paper is the advection-diffusion equation can be solved by using Adomian Laplace decomposition method.Keywords: Differential Equation, Advection-Diffusion Equation, Laplace Adomian Decomposition Method.

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Jimoh, AbdulAzeez Kayode, and Aolat Olabisi Oyedeji. "On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients." Open Journal of Mathematical Sciences 4, no. 1 (December 28, 2020): 476–84. http://dx.doi.org/10.30538/oms2020.0138.

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This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

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Mungkasi, Sudi, and I. Made Wicaksana Ekaputra. "Adomian decomposition method for solving initial value problems in vibration models." MATEC Web of Conferences 159 (2018): 02007. http://dx.doi.org/10.1051/matecconf/201815902007.

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A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method.

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Ajibade, Abiodun O., and Jeremiah Jerry Gambo. "Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium." Multidiscipline Modeling in Materials and Structures 15, no. 3 (May 7, 2019): 673–84. http://dx.doi.org/10.1108/mmms-08-2018-0153.

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Purpose The purpose of this paper is to analyze magnetohydrodynamics fully developed natural convection heat-generating/absorbing slip flow through a porous medium. Adomian decomposition method was applied to find the solutions to the problem. Design/methodology/approach In this study, Adomian decomposition method was used. Findings Results show that heat generation parameter enhanced the temperature and velocity of the fluid in the annulus. Moreover, slip effect parameter increases the velocity of the fluid. Originality/value Originality is in the application of Adomian decomposition method which allowed the slip at interface.

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Khan, Yasir, F. Naeem, and Zdeněk Šmarda. "A Novel Iterative Scheme and Its Application to Differential Equations." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/605376.

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The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

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Chang, Shih Hsiang. "Numerical Comparison of Methods for Solving Boundary Layer Problems in Hydrodynamics." Applied Mechanics and Materials 284-287 (January 2013): 508–12. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.508.

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This paper presents a numerical comparison between the differential transform method and the modified Adomian decomposition method for solving the boundary layer problems arising in hydrodynamics. The results show that the differential transform method and modified Adomian decomposition method are easier and more reliable to use in solving this type of problem and provides accurate data as compared with those obtained by other numerical methods.

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Khan, Yasir, and Francis Austin. "Application of the Laplace Decomposition Method to Nonlinear Homogeneous and Non-Homogenous Advection Equations." Zeitschrift für Naturforschung A 65, no. 10 (October 1, 2010): 849–53. http://dx.doi.org/10.1515/zna-2010-1011.

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In this paper, we apply the Laplace decomposition method to obtain series solutions of nonlinear advection equations. The equations are Laplace transformed and the nonlinear terms are represented by Adomian polynomials. The results are in good agreement with those obtained by the Adomian decomposition method and the variational iteration method but the convergence is faster.

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Subartini, Betty, Ira Sumiati, Sukono Sukono, Riaman Riaman, and Ibrahim Mohammed Sulaiman. "Combined Adomian Decomposition Method with Integral Transform." Mathematics and Statistics 9, no. 6 (November 2021): 976–83. http://dx.doi.org/10.13189/ms.2021.090613.

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SEMINARA, SILVIA, and MARIA INES TROPAREVSKY. "CONVERGENCE OF ADOMIAN DECOMPOSITION METHOD FOR PDES." Poincare Journal of Analysis and Applications 03, no. 01 (June 29, 2016): 1–12. http://dx.doi.org/10.46753/pjaa.2016.v03i01.001.

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Kutafina, Ekaterina. "Taylor series for the Adomian decomposition method." International Journal of Computer Mathematics 88, no. 17 (November 2011): 3677–84. http://dx.doi.org/10.1080/00207160.2011.611880.

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Grzymkowski, Radosław, and Damian Słota. "Stefan problem solved by Adomian decomposition method." International Journal of Computer Mathematics 82, no. 7 (July 2005): 851–56. http://dx.doi.org/10.1080/00207160512331331075.

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Wazwaz, Abdul-Majid. "A reliable modification of Adomian decomposition method." Applied Mathematics and Computation 102, no. 1 (July 1999): 77–86. http://dx.doi.org/10.1016/s0096-3003(98)10024-3.

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Hosseini, M. M., and H. Nasabzadeh. "On the convergence of Adomian decomposition method." Applied Mathematics and Computation 182, no. 1 (November 2006): 536–43. http://dx.doi.org/10.1016/j.amc.2006.04.015.

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Layeni, O. P. "Remark on modifications of Adomian decomposition method." Applied Mathematics and Computation 197, no. 1 (March 2008): 167–71. http://dx.doi.org/10.1016/j.amc.2007.07.058.

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Turkyilmazoglu, Mustafa. "Parametrized Adomian Decomposition Method with Optimum Convergence." ACM Transactions on Modeling and Computer Simulation 27, no. 4 (December 20, 2017): 1–22. http://dx.doi.org/10.1145/3106373.

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Al-Mazmumy, Mariam A. "Adomian Decomposition Method for Solving Goursat's Problems." Applied Mathematics 02, no. 08 (2011): 975–80. http://dx.doi.org/10.4236/am.2011.28134.

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Moussa, Yaya, Youssouf Pare, Pierre Clovis Nitiema, and Blaise Some. "NEW APPROACH OF THE ADOMIAN DECOMPOSITION METHOD." International Journal of Numerical Methods and Applications 16, no. 1 (June 2, 2017): 1–10. http://dx.doi.org/10.17654/nm016010001.

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Alizadeh, Ali, and Sohrab Effati. "Modified Adomian decomposition method for solving fractional optimal control problems." Transactions of the Institute of Measurement and Control 40, no. 6 (April 19, 2017): 2054–61. http://dx.doi.org/10.1177/0142331217700243.

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In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian decomposition method by examining several illustrative test problems.

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Dhaigude, D. B., and Gunvant A. Birajdar. "Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method." Advances in Applied Mathematics and Mechanics 6, no. 01 (February 2014): 107–19. http://dx.doi.org/10.4208/aamm.12-m12105.

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AbstractIn this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation. The obtained solution is verified by comparison with exact solution whenα= 1.

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Xie, Lie-jun. "A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/795015.

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We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. The results obtained indicate that the new modification is effective and promising.

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