Efficient Modification of the Decomposition Method for Solving a System of PDEs

  • L. N. M. Tawfiq Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of Baghdad
  • Z. H. Kareem Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of Baghdad
Keywords: System of PDEs, Decomposition Technique, Convergence Analysis

Abstract

     This paper presents an analysis solution for systems of partial differential equations using a new modification of the decomposition method to overcome the computational difficulties. Convergence of series solution was discussed with two illustrated examples, and the method showed a high-precision, being a fast approach to solve the non-linear system of PDEs with initial conditions. There is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. The method does not require any discretization or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented, with high accuracy and rapid convergence to the exact solution, compared with other methods that can be used to solve systems of PDEs.

Published
2021-09-30
How to Cite
Tawfiq, L. N. M., & Kareem, Z. H. (2021). Efficient Modification of the Decomposition Method for Solving a System of PDEs. Iraqi Journal of Science, 62(9), 3061-3070. https://doi.org/10.24996/ijs.2021.62.9.21
Section
Mathematics