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All Journal Journal of Multidisciplinary Science: MIKAILALSYS Mikailalsys Journal of Mathematics and Statistics
T., Shaukuna T.
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Engineering Environmental Science Mathematics Mechanical Engineering Physics Social Sciences Other

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

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.7492

Abstract

Partial Differential Equations (PDEs) are fundamental tools for modeling dynamic behaviors in physical, chemical, and engineering systems. However, solving nonlinear PDEs poses significant challenges due to the lack of closed-form solutions and the computational limitations of classical numerical approaches. This study introduces the Modified Adomian Decomposition Method (MADM) as an effective semi-analytical technique for solving both linear and nonlinear PDEs, with applications to the Advection, Burgers’, and Sine-Gordon equations. MADM enhances the classical Adomian Decomposition Method by incorporating refined recursive structures and inverse operators, which improve the convergence rate and simplify the solution process. The results demonstrate that MADM provides highly accurate solutions, often matching known exact solutions, and exhibits faster convergence compared to existing methods. Comparative analysis with the Variational Iteration Method (VIM) and the New Iteration Method (NIM) further highlights MADM’s computational efficiency and precision. These findings establish MADM as a robust and reliable tool for addressing complex PDEs across various scientific domains.
Co-Authors Abdulkarim, Muhammad B, Mwaput D. B., Mwaput D. M., Nasir U. Musa, Abubakar N., Sanda L. O., Okai J. S., Gidado A. T., Danjuma U., Mujahid A. Y., Hafsat U.