Stability studies of numerical methods for partial differential equations
| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Sao Paulo, Dept Matemat Aplicada & Estatist, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Fed Parana, Dept Matemat, BR-80060000 Curitiba, Parana - Brazil
[3] Univ Strathclyde, Dept Math, Glasgow, Lanark - Scotland
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS; v. 15, n. 10, p. 945-967, DEC 2008. |
| Web of Science Citations: | 5 |
| Abstract | |
This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley \& Sons, Ltd. (AU) | |
| FAPESP's process: | 04/16064-9 - Mechanics of non-stationary fluids: applications in aeronautics and rheology |
| Grantee: | José Alberto Cuminato |
| Support type: | Research Projects - Thematic Grants |