Open AccessEfficient Modification of the Decomposition Method for Solving a System of PDEs
Author(s) -
L. N. M. Tawfiq,
Z. H. Kareem
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.9.21
Subject(s) - adomian decomposition method , convergence (economics) , discretization , partial differential equation , decomposition method (queueing theory) , nonlinear system , mathematics , series (stratigraphy) , decomposition , linear system , mathematical optimization , computer science , algorithm , mathematical analysis , paleontology , ecology , physics , discrete mathematics , quantum mechanics , economics , biology , economic growth
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.