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

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.

Design an efficient neural network for solving steady state problems

“…Hoda and Nagla [41] used a multilayer ANN technique to address mixed BVPs. Mai-Duy and Tran-Cong in [39] introduced ANN with a radial basis function of type multi quadric for solving ODEs and elliptic PDEs. Jianye et al in [5] employed ANN with RBF to solve elliptical PDEs.…”

Efficient Approach for Solving (2+1) D- Differential Equations

“…In recent years, numerous scholars have obtained higherdimensional PDEs for Rossby solitary waves to explain the wave phenomenon in large-scale atmospheres and oceans. Yang et al 9 Many methods for solving (2+1)D-PDEs such as variable separation approach 12 , hyperbola function method 13 , expanded ( 𝐺 𝐺 2 ⁄ ) expansion method 14 , extended F-expansion method 15 , and complex method 16,17 , a Darboux Transformation 18,19 . In this paper, the researchers will use a stunner method to solve partial differential equations with (2+1)-dimension and obtain distinct and accurate analytical results.…”