Relevant bibliographies by topics / Adomian decomposition method (ADM)

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  2. Dissertations / Theses
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Academic literature on the topic 'Adomian decomposition method (ADM)'

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Published: 3 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Adomian decomposition method (ADM)"

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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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Ul Haq, Irfan. "Apply Adomian Decomposition Method (ADM) and Haar Wavelet Method (HWM) for Applications of linear Differential Equations." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 12 (2024): 1–7. https://doi.org/10.55041/ijsrem39618.

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In this work, the numerical solution of the equations arising in simple harmonic motion and free oscillation is found using the Adomian decomposition method (ADM). For comparison analysis, the Haar wavelet method (HWM) is used. Some numerical examples have been performed to illustrate the accuracy of the present work. Keywords: Oscillatory motion, Adomian decomposition method (ADM), Haar wavelet method (HWM), Simple Pendulum
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Muhammad, Rebwar, Rostam Saeed, and Davron Juraev. "New Algorithm for Computing Adomian’s Polynomials to Solve Coupled Hirota System." Journal of Zankoy Sulaimani - Part A 24, no. 1 (2022): 38–54. http://dx.doi.org/10.17656/jzs.10868.

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In this paper, when compared to the normal Adomian decomposition approach, we updated the method of calculating Adomian's polynomial to discover the numerical solution for a non-linear coupled Hirota system (CHS) with fewer components, improved accuracy, and faster convergence (ADM). The novel algorithm offers a viable way to computing Adomian polynomials for all types of non-linearity. We can see that these two methods are both effective for solving non-linear CHS, however, the result provided by our new algorithm is superior to that obtained by the classic Adomian decomposition method. Maple 15 was utilized to do calculations in our work.
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Yousef, Ali Sulaiman Alsulaiman, and M. D. Al-Eybani Ahmad. "Solve the Second Order Ordinary Differential Equations by Adomian Decomposition Method." International Journal of Mathematics and Physical Sciences Research 11, no. 1 (2023): 6–9. https://doi.org/10.5281/zenodo.7907545.

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<strong>Abstract:</strong> The Adomian decomposition model (ADM) is described by Evans and Raslan (2005) as a semi-analytical model used to solve partial and ordinary non-linear differentials. ADM was designed by George Adomian between the 1970s and the 1990s (Hosseini &amp; Nasabzadeh, 2007) whilst working at the University of Georgia&rsquo;s Applied Mathematics department. <strong>Keywords:</strong> Ordinary Differential - Differential Equations - Adomian Decomposition Method. <strong>Title:</strong> Solve the Second Order Ordinary Differential Equations by Adomian Decomposition Method <strong>Author:</strong> Yousef Ali Sulaiman Alsulaiman, Ahmad M. D. Al-Eybani <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 11, Issue 1, April 2023 - September 2023</strong> <strong>Page No: 6-9</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 08-May-2023</strong> <strong>DOI: https://doi.org/10.5281/zenodo.7907545</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/solve-the-second-order-ordinary-differential-equations-by-adomian-decomposition-method</strong>
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Mohammed, Ali Qasem Mohsen, Abdalrahim Ahmed Dawood Arafa, and Qaid Hasan Yahya. "Solving A simple Harmonic Oscillator Equation by Adomian Decomposition Method." Solving A simple Harmonic Oscillator Equation by Adomian Decomposition Method 13, no. 1 (2025): 61–65. https://doi.org/10.5281/zenodo.15494710.

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<strong>Abstract:</strong> In this paper&sbquo; we will display Adomian decomposition method (ADM) for solving a simple harmonic oscillator equation∙ It is shown that the Adomian decomposition method (ADM) efficiency&sbquo; simple&sbquo; easy to use in solving physical equation.&nbsp; The proposed method can be applied to linear problem∙ Some examples were presented to show the ability of the method for linear ordinary differential physical equations∙ <strong>Keywords:</strong> Adomian decomposition method&sbquo; harmonic oscillator schordinger equation&sbquo; physical equation. <strong>Title:</strong> Solving A simple Harmonic Oscillator Equation by Adomian Decomposition Method <strong>Author:</strong> Mohammed Ali Qasem Mohsen, Arafa Abdalrahim Ahmed Dawood, Yahya Qaid Hasan <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 13, Issue 1, April 2025 - September 2025</strong> <strong>Page No: 61-65</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 23-May-2025</strong> <strong>DOI: https://doi.org/10.5281/zenodo.15494710</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/solving-a-simple-harmonic-oscillator-equation-by-adomian-decomposition-method</strong>
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Mohammed, Ali Qasem Mohsen, and Abdalrahim Ahmed Dawood Arafa. "On the weight function for the Chebyshev equation of the first kind by the Adomian decomposition method." International Journal of Mathematics and Physical Sciences Research 13, no. 1 (2025): 66–69. https://doi.org/10.5281/zenodo.15494954.

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<strong>Abstract:</strong> In this paper, we study the use of the Adomian decomposition method (ADM) to solve the Chebyshev equation of the first kind. We show that the ADM can be used to obtain a series solution for the equation, and that the weight function for the series can be chosen to improve the accuracy of the solution. We studied the weight of Chebyshev differential equations using the Adomian decomposition method and show that the ADM is a more efficient and accurate method. <strong>Keywords:</strong> Adomian decomposition method, Chebyshev equation from first kind, weight function, Chebyshev polynomial. <strong>Title:</strong> On the weight function for the Chebyshev equation of the first kind by the Adomian decomposition method <strong>Author:</strong> Mohammed Ali Qasem Mohsen&sbquo; Arafa Abdalrahim Ahmed Dawood <strong>International Journal of Mathematics and Physical Sciences Research&nbsp;&nbsp; </strong> <strong>ISSN 2348-5736 (Online)</strong> <strong>Vol. 13, Issue 1, April 2025 - September 2025</strong> <strong>Page No: 66-69</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 23-May-2025</strong> <strong>DOI: </strong><strong>https://doi.org/10.5281/zenodo.15494954</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/on-the-weight-function-for-the-chebyshev-equation-of-the-first-kind-by-the-adomian-decomposition-method</strong>
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Pandey, Kanti. "Adomian Decomposition Method- a brief introduction." Anusandhaan - Vigyaan Shodh Patrika 7, no. 01 (2019): 92–98. https://doi.org/10.22445/avsp.v7il.17.

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In present article, an attempt is made to give a brief introduction of Adomian Decomposition Method(ADM) for solving differential equations. Advantage and accuracy of the method is shown by solving some examples.
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Turkyilmazoglu, Mustafa. "Accelerating the convergence of Adomian decomposition method (ADM)." Journal of Computational Science 31 (February 2019): 54–59. http://dx.doi.org/10.1016/j.jocs.2018.12.014.

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ANSARI, ASIYA, and NAJMUDDIN AHMAD. "NUMERICAL ACCURACY OF FREDHOLM LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY USING ADOMIAN DECOMPOSITION METHOD, MODIFIED ADOMIAN DECOMPOSITION METHOD AND VARIATIONAL ITERATION METHOD." Journal of Science and Arts 23, no. 3 (2023): 625–38. http://dx.doi.org/10.46939/j.sci.arts-23.3-a05.

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In this article, we present as a comparative result of Adomian Decomposition Method (ADM), Modified Adomian Decomposition Method (MADM) and Variational Iteration Method (VIM). These methods used for developed to find the analytical approximate solution of linear Fredholm integro-differential equations. The main purpose of this paper was to show a better method for Numerical equations which does not give easily analytical solution. So, in this paper, we find approximate solutions of linear Fredholm integro-differential equations. We explain the convergence of ADM, MADM and VIM by using examples of a deterministic model by graphs and tables. All the calculations performed by the help of MATLAB (2018) Version 9.4.
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Bildik, Necdet, and Mustafa Inc. "A Comparison between Adomian Decomposition and Tau Methods." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/621019.

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We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.
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Dissertations / Theses on the topic "Adomian decomposition method (ADM)"

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Holmquist, Sonia. "AN EXAMINATION OF THE EFFECTIVENESS OF THE ADOMIAN DECOMPOSITION METHOD IN FLUID DYNAMIC APPLICATIONS." Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2524.

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Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender's delta-perturbation method.<br>Ph.D.<br>Department of Mathematics<br>Sciences<br>Mathematics PhD
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McKee, Alex Clive Seymoore. "Analytical solutions of orientation aggregation models, multiple solutions and path following with the Adomian decomposition method." Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/7349.

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In this work we apply the Adomian decomposition method to an orientation aggregation problem modelling the time distribution of filaments. We find analytical solutions under certain specific criteria and programmatically implement the Adomian method to two variants of the orientation aggregation model. We extend the utility of the Adomian decomposition method beyond its original capability to enable it to converge to more than one solution of a nonlinear problem and further to be used as a corrector in path following bifurcation problems.
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Šustková, Apolena. "Řešení obyčejných diferenciálních rovnic neceločíselného řádu metodou Adomianova rozkladu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445455.

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This master's thesis deals with solving fractional-order ordinary differential equations by the Adomian decomposition method. A part of the work is therefore devoted to the theory of equations containing differential operators of non-integer order, especially the Caputo operator. The next part is devoted to the Adomian decomposition method itself, its properties and implementation in the case of Chen system. The work also deals with bifurcation analysis of this system, both for integer and non-integer case. One of the objectives is to clarify the discrepancy in the literature concerning the fractional-order Chen system, where experiments based on the use of the Adomian decomposition method give different results for certain input parameters compared with numerical methods. The clarification of this discrepancy is based on recent theoretical knowledge in the field of fractional-order differential equations and their systems. The conclusions are supported by numerical experiments, own code implementing the Adomian decomposition method on the Chen system was used.
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Ladeia, Cibele Aparecida. "A equação de transferência radiativa condutiva em geometria cilíndrica para o problema do escape do lançamento de foguetes." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/152738.

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Nesta contribuição apresentamos uma solução para a equação de transferência radiativa condutiva em geometria cilíndrica. Esta solução é aplicada para simular a radiação e campo de temperatura juntamente com o transporte de energia radiativa e condutiva proveniente do escape liberado em lançamentos de foguetes. Para este fim, discutimos uma abordagem semianalítica reduzindo a equação original, que é contínua nas variáveis angulares, numa equação semelhante ao problema SN da transferência radiativa condutiva. A solução é construída usando um método de composição por transformada de Laplace e o método da decomposição de Adomian. O esquema recursivo ´e apresentado para o sistema de equações de ordenadas duplamente discretas juntamente com as dependências dos parâmetros e suas influências sobre a convergência heurística da solução. A solução obtida, em seguida, permite construir o campo próximo relevante para caracterizar o termo fonte para problemas de dispersão ao ajustar os parâmetros do modelo, tais como, emissividade, refletividade, albedo e outros, em comparação com a observação, que são relevantes para os processos de dispersão de campo distante e podem ser manipulados de forma independente do presente problema. Além do método de solução, também relatamos sobre algumas soluções e simulações numéricas.<br>In this contribution we present a solution for the radiative conductive transfer equation in cylinder geometry. This solution is applied to simulate the radiation and temperature field together with conductive and radiative energy transport originated from the exhaust released in rocket launches. To this end we discuss a semi-analytical approach reducing the original equation, which is continuous in the angular variables, into an equation similar to the SN radiative conductive transfer problem. The solution is constructed using a composite method by Laplace transform and Adomian decomposition method. The recursive scheme is presented for the doubly discrete ordinate equations system together with parameter dependencies and their influence on heuristic convergence of the solution. The obtained solution allows then to construct the relevant near field to characterize the source term for dispersion problems when adjusting the model parameters such as emissivity, reflectivity, albedo and others in comparison to the observation, that are relevant for far field dispersion processes and may be handled independently from the present problem. In addition to the solution method we also report some solutions and numerical simulations.
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Archalousová, Olga. "Singulární počáteční úloha pro obyčejné diferenciální a integrodiferenciální rovnice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-233525.

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The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.
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Basto, Mário João Freitas de Sousa. "Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation." Doctoral thesis, 2006. http://hdl.handle.net/10216/12555.

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Basto, Mário João Freitas de Sousa. "Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation." Tese, 2006. http://hdl.handle.net/10216/12555.

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Pa-YeeTsai and 蔡培毅. "Applications of the Hybrid Laplace Adomian Decomposition Method to Nonlinear Physical Systems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/08208509569007412239.

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博士<br>國立成功大學<br>機械工程學系碩博士班<br>98<br>The Laplace Adomian decomposition method (LADM) combines the numerical Laplace transform algorithm and the Admoian decomposition method (ADM). The truncated series solution solved by the LADM diverges rapidly as the applicable domain increases. However, the Pad? approximant extends the domain of the truncated series solution to obtain better accuracy and convergence. In this paper, a hybrid method of the LADM combined with the Pad? approximant, named the hybrid Laplace Adomian decomposition method is proposed to solve the nonlinear physical systems to demonstrate efficient and reliable results. The linearization and small parameter assumptions are unnecessary for solving the nonlinear system problems by the hybrid Laplace Adomian decomposition method. The LADM─Pad? approximant solution is easy to obtain to demonstrate a real nonlinear physical phenomenon, and the transformation of the boundary value conditions into an initial value problem is also unnecessary when solving a boundary value problem. Furthermore, the LADM─Pad? approximant solution is able to demonstrate a nonlinear physical system by an algebra form. So the calculation is no like the numerical method that every value needs to be known every time. The hybrid Laplace Adomian decomposition method has been successfully applied to solve various nonlinear problems such as, nonlinear pendulum systems, nonlinear oscillation systems, nonlinear control systems, and nonlinear fluid dynamic systems. The LADM-Pad? approximant solutions demonstrate efficient and reliable results and have been shown a good accuracy and convergence in comparison with the exact solutions and other numerical method solutions. Moreover, the LADM─Pad? approximant solutions have been demonstrated not only the superiority of the accuracy and convergence over both the ADM and LADM solutions, but also extended the applicable domain to overcome their drawbacks.
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Hsu, Jung-Chang, and 徐榮昌. "Application of the Adomian Modified Decomposition Method to the Free Vibrations of Beams." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/45660886473944714312.

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博士<br>國立成功大學<br>機械工程學系碩博士班<br>97<br>The paper solves the eigenvalue problems and deals with the free vibration problems by using the Adomian decomposition method (ADM) and Adomian modified decomposition method (AMDM). First, using the ADM, the eigenvalues and normalized eigenfunctions for the Strum-Liouville eigenvalue problem are solved, and the governing differential equation becomes a recursive algebraic equation and boundary conditions become simple algebraic frequency equations which are suitable for symbolic computation. Moreover, after some simple algebraic operations on these frequency equations any th natural frequency, the closed form series solution of any th mode shape can be obtained. Second, the free vibration problems of Euler-Bernoulli beam under various supporting conditions are discussed. Third, using the AMDM, the free vibration problems of an elastically restrained non-uniform Euler-Bernoulli beam with tip mass of rotatory inertia and eccentricity resting on an elastic foundation and subjected to an axial load are proposed. Some numerical results are given to illustrate the influence of the physical parameters on the natural frequencies of the dynamic system. Finally, this paper deals with free vibration problems of non-uniform Timoshenko beams. In this paper, the computed results agree well with those analytical and numerical results given in the literature. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simple and more straightforward than the other analyses.
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Yu-ShengChang and 張又升. "Applications of the Hybrid Laplace Adomian Decomposition Method to Nonlinear Heat Transfer Problems." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/02149396582383943770.

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碩士<br>國立成功大學<br>機械工程學系<br>102<br>When we try to solve physical problems ,we usually build math models to approach our problems. Nonlinear terms are very common both in physical problems and math models, but they will complicate the solving process. In this paper , we use LADM method to solve nonlinear heat transfer problems. We have two cases , nonlinear fin system and nonlinear continuously moving plates system. Some parameters like Convection, radiation, slope of the thermal conductivity-temperature curve , slope of the surface emissivity-temperature curve are discussed. We found when dimensionless numbers as following increase：Nc、Nr 、B(which presents the conventional intensity to conductional intensity、radiative intensity to conductional intensity、surface emission , respectively)will speed up heat transfer in fin or plate. Dimensionless number A(which presents slope of the thermal conductivity-temperature curve)increases will make heat transfer more faster in fin or plate. Dimensionless number Pe(which presents peclet number) increases (if we have a constant fin length or plate length and constant thermal diffusivity )will make final temperature higher. Assuming a power law variation (decided by parameter m ) of the convection coefficient . Nonlinear terms can also be increased by parameter m . In conclusion, LADM is an effective way to solve nonlinear system. Following this paper , we can know more in material or fluid selecting.
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Books on the topic "Adomian decomposition method (ADM)"

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Stephan, Andy. Die Adomian decomposition method zum Lösen nichtlinearer Gleichungen und Gleichungssysteme. GRIN Verlag GmbH, 2009.

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Book chapters on the topic "Adomian decomposition method (ADM)"

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Keskin, Ali Ümit. "Adomian Decomposition Method (ADM)." In Boundary Value Problems for Engineers. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21080-9_7.

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Sun, Kehui, Shaobo He, and Huihai Wang. "Adomian Decomposition Method." In Solution and Characteristic Analysis of Fractional-Order Chaotic Systems. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3273-1_4.

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Das, Prakash Kumar, and M. M. Panja. "An Improved Adomian Decomposition Method for Nonlinear ODEs." In Applied Mathematics. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2547-8_18.

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Kataria, K. K., and P. Vellaisamy. "Adomian Decomposition Method and Fractional Poisson Processes: A Survey." In Trends in Mathematics. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9227-6_2.

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Schmitt, Andreas, Martin Schreiber, and Michael Schäfer. "Additional Degrees of Parallelism Within the Adomian Decomposition Method." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93891-2_7.

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Goyal, Kavita, and Meenal Singhal. "Adomian Decomposition Method for Thermal Analysis of a Furnace." In Advances in Engineering Research and Application. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04792-4_20.

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Kelil, Abey S., and Appanah R. Appadu. "Shehu-Adomian Decomposition Method for Dispersive KdV-Type Equations." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-8177-6_8.

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Khandelwal, Yogesh, Gajendra Kumar Mahawar, and Rachana Khandelwal. "Fractional Models by Using Adomian Decomposition Method with Mahgoub Transformation." In Advances in Intelligent Systems and Computing. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5414-8_12.

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Anakira, Nidal, Gada Bani-Hani, Osama Ababneh, Ali Jameel, and Khamis Al-Kalbani. "Modified Adomian Decomposition Method for Solving Volterra Integro-Differential Equations." In Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4876-1_23.

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Bhattacharya, P., and S. Pal. "Solution of insect population model by using Laplace Adomian decomposition method." In Computational Science and Engineering. CRC Press, 2016. http://dx.doi.org/10.1201/9781315375021-33.

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Conference papers on the topic "Adomian decomposition method (ADM)"

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Hussein ALI, Ali, and Ali Qasem THAJIL. "SOLVING SECOND ORDER ORDINARY DIFFERENTIAL EQUATION BY FINITE DIFFERENCE METHOD , ADOMIAN DECOMPOSITION METHOD AND GALERKIN- METHOD." In VII. INTERNATIONAL SCIENTIFIC CONGRESSOF PURE,APPLIEDANDTECHNOLOGICAL SCIENCES. Rimar Academy, 2023. http://dx.doi.org/10.47832/minarcongress7-4.

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In this study ,three numerical methods presented for solving ordinary differential equations of the second order: Finite Difference Method (FDM), Domain Analysis Method (ADM) and Galerkin Method. Then we conduct a comparative study between the three methods with the -exact solution-. The study was conducted through illustrative examples. The study showed that ADM is identical to the exact solution. Therefore, ADM is a safe and effective numerical technique for solving problems in various sciences.
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Farshidianfar, Anooshiravan, Rassoul Tabassian, Omid Kazemzadeh Khoee, and Sayed Javadorreza Noei. "Solving Free Vibration of Stepped Beam by Using the Adomian Decomposition Method." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-25335.

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This paper studies the free vibration of Euler-Bernoulli stepped beam with different cross-sections and also different materials for each section. In this work, a new approach called Adomian decomposition method (ADM) is used to deal with vibration problem. Natural frequencies of stepped beam are obtained with high accuracy using this method. Numerical results are validated by ANSYS.10 and proper convergence is observed between results. Effects of various parameters like step ratio on natural frequency are discussed. Applying this method on free vibration of stepped beam constructs a systematic procedure which is completely straightforward and could calculate both low and high mode frequency with appropriate accuracy.
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Biazar, Jafar, Zainab Ayati, and Hamideh Ebrahimi. "Comparing Homotopy Perturbation Method and Adomian Decomposition Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991054.

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Constantinescu, Radu, Carmen Ionescu, Mihai Stoicescu, Madalin Bunoiu, and Iosif Malaescu. "Adomian Decomposition Method for Quark Gluon Plasma Model." In PHYSICS CONFERENCE TIM-10. AIP, 2011. http://dx.doi.org/10.1063/1.3647049.

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Gurrala, Gurunath, Aleksandar Dimitrovski, Srdjan Simunovic, and Pannala Sreekanth. "Numeric modified adomian decomposition method for power system simulations." In 2016 IEEE International Conference on Power System Technology (POWERCON). IEEE, 2016. http://dx.doi.org/10.1109/powercon.2016.7753948.

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Mahiddin, Norhasimah, Siti Aishah Hashim Ali, Kamel Ariffin Mohd Atan, and Isthrinayagy S. Krishnarajah. "Modeling of Tumor Growth Based on Adomian Decomposition Method." In INTERNATIONAL CONFERENCE ON MATHEMATICAL BIOLOGY 2007: ICMB07. AIP, 2008. http://dx.doi.org/10.1063/1.2883872.

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Mungkasi, Sudi, and Maria Febronia Sedho Dheno. "Adomian decomposition method used to solve the gravity wave equations." In INTERNATIONAL CONFERENCE ON ENGINEERING, SCIENCE AND NANOTECHNOLOGY 2016 (ICESNANO 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4968356.

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Dispini, Meta, and Sudi Mungkasi. "Adomian decomposition method used to solve the shallow water equations." In THE 2016 CONFERENCE ON FUNDAMENTAL AND APPLIED SCIENCE FOR ADVANCED TECHNOLOGY (CONFAST 2016): Proceeding of ConFAST 2016 Conference Series: International Conference on Physics and Applied Physics Research (ICPR 2016), International Conference on Industrial Biology (ICIBio 2016), and International Conference on Information System and Applied Mathematics (ICIAMath 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4953980.

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Demir, Duygu Dönmez, and Erhan Koca. "The solution of a string model by adomian decomposition method." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912592.

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Duan, Nan, and Kai Sun. "Power system simulation using the multi-stage adomian decomposition method." In 2017 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2017. http://dx.doi.org/10.1109/pesgm.2017.8273740.

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