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Abstract

In this paper, the mixed Galerkin- implicit difference method (MGIFDM) is used to solve a couple of nonlinear systems of parabolic partial differential equations with constant coefficients which are abbreviated by (CNPSCC). At first the weak form of the CNPSCC is formulated and then it is discretized using the proposed method, the method mixes the Galerkin finite element method (GFEM) in space variables with the implicit finite difference method (IFDM) in time variables, so the method was named by MGIFDM. At any discrete time tj the method transforms the CNPSCC into a couple Galerkin nonlinear algebraic system (CGNAS), which is solved by applying the predictor-corrector techniques, this technique is used to reduce the “nonlinear” CGNAS into a couple of linear Galerkin system algebraic, of course at any discrete time tj. Then the Cholesky decomposition method is utilized to solve it (at any time tj). The convergence theorem is given and demonstrated, to show the convergence of the solutions to the proposed problem. Two examples are given to illustrate and examine the method, and the results are given by tables and by figures and show the efficiency and accuracy of the proposed method.

Keywords

Coupled nonlinear parabolic system, Cholesky decomposition method, Galerkin method, Implicit difference method, Predictor and corrector techniques

Subject Area

Mathematics

Article Type

Article

First Page

2350

Last Page

2359

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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