Implicit Finite Differences Method for Solving Couple Nonlinear parabolic system with Constant Coefficients
Keywords:
Coupled Nonlinear Parabolic System, Implicit Finite Difference Method, Consistency, ConvergenceAbstract
In this paper, the implicit finite differences method (IFDM) is used to solve couple of nonlinear parabolic system with constant coefficients (CNPS). At any discrete time the proposed method is transforms the CNPS into a couple nonlinear algebraic system (CNAS), which is solved by applying the predictor- corrector techniques (PCT). This technique reduces the CNAS into a linear system and where the Cholesky decomposition (ChDe) is utilized to solve it at any time . The consistency and the convergence of the method are studied. Two examples are given and are solved using the IFDM to compare their results with the results obtained from solving the same examples but by utilizing the mixed Galerkin - Implicit Differences Methods (MGIDM). The results show that the MGIDM is more accurate than the IFDM.
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Copyright (c) 2024 Jamil Al-Hawasy (Author)
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