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Volume 7, Issue 4
A Comparative Analysis Between Adomian Decomposition Method and Differential Transformation Method for Solving Some Second-Order Ordinary Differential Equations

Entesar Ali AL-Huwaisek, Nuha Mohammed Dabwan & Yahya Qaid Hasan

DOI: 10.12150/jnma.2025.1353

J. Nonl. Mod. Anal., 7 (2025), pp. 1353-1368.

Published online: 2025-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The differential transformation method (DTM) and Adomian decomposition method (ADM) are two numerical methods that can be used to solve various differential equations. In this work, we compare the accuracy, convergence, and computational complexity of these two methods by using them to solve second-order nonlinear equations using a new differential operator for the second-order equation. We also used both methods to solve second-order nonlinear differential equations.

  • Keywords

Differential transformation method, Adomian decomposition method, second-order ordinary differential equations.

  • AMS Subject Headings

34Nxx, 34N05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1353, author = {AL-Huwaisek , Entesar AliDabwan , Nuha Mohammed and Hasan , Yahya Qaid}, title = {A Comparative Analysis Between Adomian Decomposition Method and Differential Transformation Method for Solving Some Second-Order Ordinary Differential Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1353--1368}, abstract = {

The differential transformation method (DTM) and Adomian decomposition method (ADM) are two numerical methods that can be used to solve various differential equations. In this work, we compare the accuracy, convergence, and computational complexity of these two methods by using them to solve second-order nonlinear equations using a new differential operator for the second-order equation. We also used both methods to solve second-order nonlinear differential equations.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1353}, url = {http://global-sci.org/intro/article_detail/jnma/24240.html} }
TY - JOUR T1 - A Comparative Analysis Between Adomian Decomposition Method and Differential Transformation Method for Solving Some Second-Order Ordinary Differential Equations AU - AL-Huwaisek , Entesar Ali AU - Dabwan , Nuha Mohammed AU - Hasan , Yahya Qaid JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 1353 EP - 1368 PY - 2025 DA - 2025/07 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1353 UR - https://global-sci.org/intro/article_detail/jnma/24240.html KW - Differential transformation method, Adomian decomposition method, second-order ordinary differential equations. AB -

The differential transformation method (DTM) and Adomian decomposition method (ADM) are two numerical methods that can be used to solve various differential equations. In this work, we compare the accuracy, convergence, and computational complexity of these two methods by using them to solve second-order nonlinear equations using a new differential operator for the second-order equation. We also used both methods to solve second-order nonlinear differential equations.

AL-Huwaisek , Entesar AliDabwan , Nuha Mohammed and Hasan , Yahya Qaid. (2025). A Comparative Analysis Between Adomian Decomposition Method and Differential Transformation Method for Solving Some Second-Order Ordinary Differential Equations. Journal of Nonlinear Modeling and Analysis. 7 (4). 1353-1368. doi:10.12150/jnma.2025.1353
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