التفاصيل البيبلوغرافية
| العنوان: |
Superconvergence of Solution Derivatives for the Shortley-Weller Difference Approximation for Parabolic Problems. |
| المؤلفون: |
Li, Z.-C.1 (AUTHOR), Fang, Q.2 (AUTHOR) fang@sci.kj.yamagata-u.ac.jp, Wang, S.3 (AUTHOR) |
| المصدر: |
Numerical Functional Analysis & Optimization. Nov/Dec2009, Vol. 30 Issue 11/12, p1360-1380. 21p. 2 Diagrams, 3 Charts. |
| مصطلحات موضوعية: |
*STOCHASTIC convergence, *SMOOTHING (Numerical analysis), *FINITE differences, *POISSON processes, *EQUATIONS |
| مستخلص: |
In [8-118, 9, 10, 11] a superconvergence analysis is derived for the smooth and singular Poisson equations by the finite difference method (FDM) using the Shortley-Weller approximation. In this article, we explore the superconvergence analysis for a parabolic equation using the Shortley-Weller approximation and the Crank-Nicolson scheme (CNS) in space and time discretization, respectively, denoted simply as FDM-CNS. The results of derivative superconvergence in [8-118, 9, 10, 11] can be extended to parabolic problems of smooth and singular solutions. The main results are as follows: when [image omitted] and [image omitted], the superconvergence rate O(h2 + k2) is derived for the solution derivatives in discrete H1 norms by the FDM-CNS on rectangular domains, where k is the time mesh spacing in the Crank-Nicolson scheme and h is the maximal mesh length of difference grids used. Note that the difference grids are not confined to be quasi-uniform, and local refinements are allowed for the solutions with unbounded derivatives. Numerical experiments are provided to support the superconvergence O(h2 + k2). [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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