Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations

Khadeejah James Audu; Lawrence Linus; Yahaya Yusuph Amuda; Sıkırulaı Akande

doi:10.38088/jise.1563076

EN

Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations

Abstract

Partial Differential Equations (PDE) help model problems in science and engineering, given their abilities to capture complex phenomena compared to Ordinary Differential Equations. This paper aims to investigate two semi-analytical techniques called the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM), how these methods can be used in practice, and to make a comparative study of the two methods for solving linear and nonlinear PDEs. The efficiency of ADM and VIM is assessed by comparing their errors relative to the exact solutions of the examined numerical experiments. The results obtained from the numerical experiments revealed that ADM proved to be a more efficient and accurate method for solving PDEs than VIM.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Analysis

Journal Section

Research Article

Authors

Khadeejah James Audu ^*
0000-0002-6986-3491
Nigeria

Lawrence Linus
0009-0005-3316-9384
Nigeria

Yahaya Yusuph Amuda
0000-0002-3410-9173
Nigeria

Sıkırulaı Akande
0000-0002-8216-744X
Nigeria

Early Pub Date

May 2, 2025

Publication Date

June 17, 2025

Submission Date

October 17, 2024

Acceptance Date

February 14, 2025

Published in Issue

Year 2025 Volume: 9 Number: 1

DOI

https://doi.org/10.38088/jise.1563076

IZ

https://izlik.org/JA89WZ27YG

Cite

RIS / Bibtex

APA

Audu, K. J., Linus, L., Amuda, Y. Y., & Akande, S. (2025). Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations. Journal of Innovative Science and Engineering, 9(1), 39-53. https://doi.org/10.38088/jise.1563076

AMA

1.Audu K J, Linus L, Amuda YY, Akande S. Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations. JISE. 2025;9(1):39-53. doi:10.38088/jise.1563076

Chicago

Audu, Khadeejah James, Lawrence Linus, Yahaya Yusuph Amuda, and Sıkırulaı Akande. 2025. “Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations”. Journal of Innovative Science and Engineering 9 (1): 39-53. https://doi.org/10.38088/jise.1563076.

EndNote

Audu K J, Linus L, Amuda YY, Akande S (June 1, 2025) Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations. Journal of Innovative Science and Engineering 9 1 39–53.

IEEE

[1]K. J. Audu, L. Linus, Y. Y. Amuda, and S. Akande, “Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations”, JISE, vol. 9, no. 1, pp. 39–53, June 2025, doi: 10.38088/jise.1563076.

ISNAD

Audu, Khadeejah James - Linus, Lawrence - Amuda, Yahaya Yusuph - Akande, Sıkırulaı. “Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations”. Journal of Innovative Science and Engineering 9/1 (June 1, 2025): 39-53. https://doi.org/10.38088/jise.1563076.

JAMA

1.Audu K J, Linus L, Amuda YY, Akande S. Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations. JISE. 2025;9:39–53.

MLA

Audu, Khadeejah James, et al. “Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations”. Journal of Innovative Science and Engineering, vol. 9, no. 1, June 2025, pp. 39-53, doi:10.38088/jise.1563076.

Vancouver

1.Khadeejah James Audu, Lawrence Linus, Yahaya Yusuph Amuda, Sıkırulaı Akande. Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations. JISE. 2025 Jun. 1;9(1):39-53. doi:10.38088/jise.1563076