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The Unconditional Convergent Difference Methods with Intrinsic Parallelism for Quasilinear Parabolic Systems with Two Dimensions
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@Article{JCM-21-41,
author = {},
title = {The Unconditional Convergent Difference Methods with Intrinsic Parallelism for Quasilinear Parabolic Systems with Two Dimensions},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {1},
pages = {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 apriori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixedpoint technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with inreinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to th eunique generalized solution of the original quasilinear parabolic problem is proved. },
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/10281.html}
}
TY - JOUR
T1 - The Unconditional Convergent Difference Methods with Intrinsic Parallelism for Quasilinear Parabolic Systems with Two Dimensions
JO - Journal of Computational Mathematics
VL - 1
SP - 41
EP - 52
PY - 2003
DA - 2003/02
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10281.html
KW - Difference Scheme
KW - Intrinsic Parallelism
KW - Two Dimensional Quasilinear Parabolic System
AB - 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 apriori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixedpoint technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with inreinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to th eunique generalized solution of the original quasilinear parabolic problem is proved.
Longjun Shen & Guangwei Yuan. (1970). The Unconditional Convergent Difference Methods with Intrinsic Parallelism for Quasilinear Parabolic Systems with Two Dimensions.
Journal of Computational Mathematics. 21 (1).
41-52.
doi:
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