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| UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE |
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Citation： |
ZHOU Yulin,SHEN Longjun,YUAN Guangwei.UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE[J].Chinese Annals of Mathematics B,2004,25(2):213~224 |
| Page view： 1189
Net amount： 841 |
Authors： |
ZHOU Yulin; SHEN Longjun;YUAN Guangwei |
Foundation： |
Project supported by China “National Key Program for Developing Basic Sciences” (No.G1999032801),
the National Natural Science Foundation of China (No.19932010), the Science and Technology Foundation
of Chinese Academy of Engineering Physics (No.20020652) and (No.ZX0107). |
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| Abstract： |
The general finite difference schemes with intrinsic parallelism
for the boundary value problem of the semilinear parabolic system
of divergence type with bounded measurable coefficients is
studied. By the approach of the discrete functional analysis, the
existence and uniqueness of the discrete vector solutions of the
nonlinear difference system with intrinsic parallelism
are proved. Moreover the unconditional stability of
the general difference schemes with intrinsic parallelism
justified in the sense of the continuous dependence of the
discrete vector solution of the difference schemes on the discrete
initial data of the original problems in the discrete
$W^{(2,1)}_2(Q_\Delta)$ norms. Finally the convergence of the
discrete vector solutions of the certain difference schemes with
intrinsic parallelism to
the unique generalized solution of the original semilinear parabolic problem
is proved. |
Keywords： |
Difference scheme, Intrinsic parallelism, Parabolic system, Stability,
Convergence |
Classification： |
65M60, 65M12 |
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