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Stability analysis of six-point finite difference schemes for the constant coefficient convective-diffusion equation

✍ Scribed by Yue-Kuen Kwok

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
426 KB
Volume
23
Category
Article
ISSN
0898-1221

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✦ Synopsis

Al:mtract--A comprehensive and systematic study is presented to derive stability properties of various two-level, six-point finite difference schemes (in particular, difference schemes of Pad~ type) for the approximation to the constant coefficient convective-ditfusion equation. First, the modified equivalent partial differential equation (MEPDE) for a general six-point difference scheme is derived.

The MEPDE provides direct information on the order of accuracy of a difference scheme. The von Neumann and matrix methods are then employed to deduce the necessary and sufficient conditions for the numerical stability for the six-point difference schemes. An unified technique is developed to find the stability regions for the difference schemes. Some new second and third order six-point difference schemes for the approximation of the constant coefficient convective-diffusion equation are presented.

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