Mixed Galerkin- Implicit Differences Methods for Solving Coupled Parabolic Boundary Value Problems with Variable Coefficients

Abstract

In this paper, an approximation technique is introduced to solve the coupled linear parabolic boundary value problems with variable coefficients by using mixed of the Galerkin finite element method in space variable with implicit finite difference method in the time variable. At any discrete time this technique is transformed the coupled linear parabolic boundary value problems with variable coefficients into a linear algebraic system which is called a Galerkin a linear algebraic system, and then it is solved using the Cholesky Decomposition. Illustration examples are presented and the results are shown by figures and tables, and show the efficiency of the proposed method.