Volume 14, Issue 4
Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic System

Y. L. Zhou

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J. Comp. Math., 14 (1996), pp. 319-335

Published online: 1996-08

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  • Abstract

The boundary value problem for the nonlinear parabolic system is solved by the finite difference method with nonuniform meshes. The existence and a priori estemates of the discrete vector solutions for the general difference schemes with unequal meshsteps are established by the fixed point technique. The absolute and relative convergence of the discrete vector solution %and the absolute and relative stability of the difference scheme are justified by a series of a priori estimates. The analysis of mentioned problems are based on the assumption of heuristic character concerning the existence of the unique smooth solution for the original problem of the nonlinear parabolic system.

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@Article{JCM-14-319, author = {}, title = {Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic System}, journal = {Journal of Computational Mathematics}, year = {1996}, volume = {14}, number = {4}, pages = {319--335}, abstract = { The boundary value problem for the nonlinear parabolic system is solved by the finite difference method with nonuniform meshes. The existence and a priori estemates of the discrete vector solutions for the general difference schemes with unequal meshsteps are established by the fixed point technique. The absolute and relative convergence of the discrete vector solution %and the absolute and relative stability of the difference scheme are justified by a series of a priori estimates. The analysis of mentioned problems are based on the assumption of heuristic character concerning the existence of the unique smooth solution for the original problem of the nonlinear parabolic system. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9242.html} }
TY - JOUR T1 - Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic System JO - Journal of Computational Mathematics VL - 4 SP - 319 EP - 335 PY - 1996 DA - 1996/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9242.html KW - AB - The boundary value problem for the nonlinear parabolic system is solved by the finite difference method with nonuniform meshes. The existence and a priori estemates of the discrete vector solutions for the general difference schemes with unequal meshsteps are established by the fixed point technique. The absolute and relative convergence of the discrete vector solution %and the absolute and relative stability of the difference scheme are justified by a series of a priori estimates. The analysis of mentioned problems are based on the assumption of heuristic character concerning the existence of the unique smooth solution for the original problem of the nonlinear parabolic system.
Y. L. Zhou. (1970). Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic System. Journal of Computational Mathematics. 14 (4). 319-335. doi:
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