One- and Two-dimensional bicompact schemes in layered media

被引：0

作者：

Kalitkin N.N. ^{[1
]}

Koryakin P.V. ^{[1
]}

机构：

[1] Institute of Mathematical Modeling, Russian Academy of Sciences, Moscow

来源：

Mathematical Models and Computer Simulations | 2010年 / 2卷 / 2期

基金：

俄罗斯基础研究基金会;

关键词：

Grid Node; Classical Scheme; Triangular Grid; Initial Profile; Integral Node;

D O I：

10.1134/S2070048210020018

中图分类号：

学科分类号：

摘要：

A new type of difference schemes, i.e., the so-called bicompact schemes, is addressed. Writing such schemes in partial differential equations is reduced to equivalent systems of ordinary differential equations. Spatial derivatives are approximated on a two-point stencil, i.e., within a single grid step. In layered media, in introducing special grids, on which all break points of coefficients are grid nodes, bicompact schemes keep their approximation. Two schemes of the Kochi problem solution for the one-dimensional heat conductivity equation are examined in detail and schemes for two-dimensional problems on arbitrary grids are given. © 2010, Pleiades Publishing, Ltd.

引用

页码：139 / 155

页数：16

共 7 条

[1] Tolstykh A.I., Compact Difference Schemes and Their Application in Aerohydrodynamic Problems, (1990)
[2] Kalitkin N.N., Koryakin P.V., Bicomponent Schemes and Stratified Mediums, Dokl. Akad. Nauk, 419, 6, pp. 1-5, (2008)
[3] Rogov B.V., Mikhailovskaya M.N., On Convergence of Contact Difference Schemes, Mat. Modelir., 20, 1, pp. 99-117, (2008)
[4] Samarskii A.A., Theory of Difference Schemes, (1989)
[5] Rosenbrock H.H., Some General Implicit Processes for the Numerical Solution of Differential Equations, Comput. J., 5, 4, pp. 329-330, (2000)
[6] Kalitkin N.N., Kuznetsov N.O., Panchenko S.L., Method of Quasiuniform Grids in Infinite Domain, Dokl. Akad. Nauk, 374, 5, pp. 598-601, (2000)
[7] Al'shina E.A., Kalitkin N.N., Calculation of Differential Operators Spectra, Dokl. Akad. Nauk, 380, 4, pp. 443-447, (2001)

← 1 →