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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Journal of Multidisciplinary Science: MIKAILALSYS
Nasir U. M.
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Environmental Science Physics Social Sciences Other

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Application of a Modified Adomian Decomposition Method for Solving Linear and Nonlinear Partial Differential Equations Okai J. O.; Abubakar Musa; Sanda L. N.; Nasir U. M.; Hafsat U. Y.; Gidado A. S.; Mwaput D. B; Danjuma T.; Shaukuna T. T.; Muhammad Abdulkarim; Mujahid A. U.
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 3 (2025): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i3.7318

Abstract

Partial Differential Equations (PDEs) are fundamental to the mathematical modeling of various physical, chemical, and engineering phenomena. However, solving nonlinear PDEs poses significant challenges due to the lack of general closed-form solutions and the limitations of traditional numerical methods. This study introduces a Modified Adomian Decomposition Method (MADM) as an effective semi-analytical approach for solving both linear and nonlinear PDEs, with specific application to the Advection, Burgers’, and Sine-Gordon equations. The MADM enhances the classical Adomian Decomposition Method (ADM) by incorporating refined recursive structures and inverse operators, leading to improved solution accuracy and convergence speed. The results demonstrate that MADM not only yields highly accurate approximations but also reproduces exact solutions in certain cases. Comparative analysis with established methods such as the Variational Iteration Method (VIM) and the New Iteration Method (NIM) reveals that MADM outperforms them in terms of computational efficiency and precision. These findings underscore MADM's potential as a robust and efficient tool for solving a wide class of complex PDEs in applied sciences and engineering.
A Hybrid Approach of the Variational Iteration Method and Adomian Decomposition Method for Solving Fractional Integro-Differential Equations Okai J. O; M. S. Adamu; Cornelius M.; Abdulmalik I.; Jeremiah A.; Nasir U. M.; Hafsat Y. U.; Abichele O.; Hassan Araga
YASIN Vol 5 No 4 (2025): YASIN: Jurnal Pendidikan dan Sosial Budaya
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i4.5720

Abstract

In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations of integer and fractional orders. This approach extends and refines the Odibat Decomposition Method (ODM) by addressing key limitations inherent in ADM and VIM—specifically, the reliance on linearization, Adomian polynomials, and Lagrange multipliers. By circumventing these computational complexities, the proposed method enables the direct and efficient construction of series solutions with improved convergence properties. The hybrid scheme is designed for broader applicability and enhanced computational simplicity, making it a powerful tool for analyzing complex integro-differential systems. Its effectiveness and robustness are demonstrated through a range of illustrative examples, confirming the method’s capability to provide accurate analytical approximations with minimal computational overhead.
Co-Authors Abdulmalik I. Abichele O. Abubakar Musa Cornelius M. Danjuma T. Gidado A. S. Hafsat U. Y. Hafsat Y. U. Hassan Araga Jeremiah A. M. S. Adamu Muhammad Abdulkarim Mujahid A. U. Mwaput D. B Okai J. O Okai J. O. Sanda L. N. Shaukuna T. T.