Solving Coupled Parabolic System by Using Galerkin - Implicit Differences Methods

Wafaa Abd  Ibrahim; Jamil A. Ali   Al-Hawasy

doi:10.24996/ijs.2025.66.9.30

Authors

Wafaa Abd Ibrahim Depart. of Mathematics, Almuqdad College of Education, University of Diyala Baqubah, Iraq
Jamil A. Ali Al-Hawasy Depart. of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.9.30

Keywords:

Coupled Parabolic System, Galerkin Finite Element Method, Implicit Finite Differences Method, Cholesky Method

Abstract

This paper deal with a technique of approximation which is insert to find the solution of a new type of couple system of constant coefficients parabolic equations (CPS) from mixing the method of finite element of Galerkin (GFEM) “in the variable of space” with the finite differences method of implicit type (IFDM) in the variable of time. Therefore, the abbreviation IGFEM is utilized to express on the method named by implicit Galerkin finite element method (IGFEM(. In this method at each discrete value of time , the CPS convert into a Galerkin system of algebraic equations (GLAS) and later it is resolved by utilizing the method of Cholesky Decomposition (ChDeM). Examples of explanations are awarded and the illustration for the results are presented through tables and figures, and they exhibit that the method which is proposed her is accurate and efficient.