Symmetry preserving numerical schemes for partial differential equations and their numerical tests

被引：29
作者：
Rebelo, Raphael [1 ]
Valiquette, Francis [2 ]
机构：
[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada
[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2013年 / 19卷 / 05期
基金：
加拿大自然科学与工程研究理事会;
关键词：
equivariant moving frames; finite difference equations; invariants; symmetry groups; 58J70; 68N06; INVARIANTIZATION; DISCRETIZATION; FOUNDATIONS; INTEGRATION;
D O I：
10.1080/10236198.2012.685470
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The method of equivariant moving frames is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for a heat equation with logarithmic source and the spherical Burgers' equation are obtained. Numerical tests show how invariant schemes can be more accurate than standard discretizations.
引用
收藏
页码：738 / 757
页数：20
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