The Unconditional Convergent Difference Methods with Intrinsic Parallelism for Quasilinear Parabolic Systems with Two Dimensions
Year: 2003
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 1 : pp. 41–52
Abstract
In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed point technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover, the convergence of the discrete vector solutions of these difference schemes to the unique generalized solution of the original quasilinear parabolic problem is proved.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-10281
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 1 : pp. 41–52
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Difference Scheme Intrinsic Parallelism Two Dimensional Quasilinear Parabolic System Existence Convergence.