Application of a Modified Adomian Decomposition Method for Solving Linear and Nonlinear Partial Differential Equations
Article Sidebar
Page Numbers:
1245-1262
Digital Object Identifier:
10.58578/mikailalsys.v3i3.7318
Viewed: 241 times
Downloaded: 134 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:Okai J. O.1*, Abubakar Musa2, Sanda L. N.3, Nasir U. M.4, Hafsat U. Y.5, Gidado A. S.6, Mwaput D. B7, Danjuma T.8, Shaukuna T. T.9, Muhammad Abdulkarim10, Mujahid A. U.11
Copyright :Authors retain copyright and grant the journal right of first publication.
Main Article Content
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.
Citation Metrics:
Downloads
Citation Metrics & Similar Scopus Articles
-
Lukpanov R.E. (2027)Evaluation of the Effect of Additives on the Workability of Concrete Mix as Part of a Study of a Modified Wall BlockKompleksnoe Ispolzovanie Mineralnogo Syra, 342(3), 100-110
-
Naemi Z. (2027)The Relationship between Second Language Learning Strategies, Learning Engagement, and Writing Skill in the Arabic Writing CurriculumLanguage Related Research, 17(4), 331-360
-
Sadati Nooshabadi S.M. (2027)Object Agreement: A Syntactic Phenomenon in Middle Persian Zoroastrian TextsLanguage Related Research, 17(4), 71-101
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Abu Arqub, O., Abo-Hammour, Z., Al-Badameh, R., & Momani, S. (2013). A reliable analytical method for solving higher-order initial value problems. Discrete Dynamics in Nature and Society, 2013, 1–14.
Adomian, G., & Rach, R. (1983). Inversion of nonlinear stochastic operators. Journal of Mathematical Analysis and Applications, 91(1), 39–46.
Bhalekar, S., & Daftardar-Gejji, V. (2010). Solving evolution equations using decomposition method. Applied Mathematics and Computation, 216(10), 2909– 2914.
Cherruault, Y. (1989). Convergence of Adomian’s method. Kybernetes, 18(2), 31–38.
Cherruault, Y., & Adomian, G. (1993). Decomposition methods: A new proof of convergence. Mathematical and Computer Modelling, 18(12), 103–106.
Duan, J.-S., Rach, R., Baleanu, D., & Wazwaz, A. M. (2012). A review of the Adomian decomposition method and its application to fractional differential equations. Communications in Fractional Calculus, 3(2), 73–99.
Evans, L. C. (2010). Partial Differential Equations (2nd ed.). American Mathematical Society.
Fang, H., He, Y., & Wang, J. (2022). Analytical solutions for nonlinear PDEs via modified decomposition approaches. Nonlinear Dynamics, 110(4), 3145–3160.
Kaya, D. (2002). The use of the Adomian decomposition method for solving specific nonlinear partial differential equations. Bulletin of the Belgian Mathematical Society - Simon Stevin, 9(3), 343–349.
Kumar, S. (2014). Modified decomposition methods for nonlinear PDEs. Applied Mathematics Letters, 37, 57–63.
LeVeque, R. J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM.
Li, W., & Pang, Y. (2020). Application of Adomian decomposition method to nonlinear systems. Advances in Continuous and Discrete Models, 2020, Article 42.
Nuruddeen, R., Abdullahi, I., & Auwal, A. (2018). Exact and approximate solutions of nonlinear PDEs via ADM. International Journal of Differential Equations, 2018, Article 747318.
Ojimadu, U. H., Usman, M. A., Olasupo, A. O., Olubanwo, O. O., Oyewole, O., Ayo, F. E., Ayodele, M. A., Sulaiman, M. A., & Ajani, A. S. (2022). Application of
Adomian decomposition methods in solving some selected nonlinear partial differential equations. Journal of the Nigerian Association of Mathematical Physics, 64, 83– 86.
Syam, M. I., Alsuwaidi, A., Alneyadi, A., AlRufai, S., & Alkhaldi, S. (2019). Implicit hybrid methods for solving fractional Riccati equation. Journal of Nonlinear Sciences and Applications, 12(2), 124–134.
Wazwaz, A. M. (2009). Partial Differential Equations and Solitary Waves Theory. Springer.