Two-level finite difference scheme of improved accuracy order for time-dependent problems of mathematical physics
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- 作者：P. N. Vabishchevich (1) vabishchevich@gmail.com
- 关键词：Key words Cauchy problem for a first ; order evolutionary equation ; operator ; difference schemes ; stability of finite difference scheme
- 刊名：Computational Mathematics and Mathematical Physics
- 出版时间：January 2010
- 出版年：2010
- 期刊代码：pc576_0965-5425
- 类别：mat
- 卷：50
- 期：1
- 页码：112-123
- 数据来源：sp
摘要
In the theory of finite difference schemes, the most complete results concerning the accuracy of approximate solutions are obtained for two- and three-level finite difference schemes that converge with the first and second order with respect to time. When the Cauchy problem is numerically solved for a system of ordinary differential equations, higher order methods are often used. Using a model problem for a parabolic equation as an example, general requirements for the selection of the finite difference approximation with respect to time are discussed. In addition to the unconditional stability requirements, extra performance criteria for finite difference schemes are presented and the concept of SM stability is introduced. Issues concerning the computational implementation of schemes having higher approximation orders are discussed. From the general point of view, various classes of finite difference schemes for time-dependent problems of mathematical physics are analyzed.