Symmetry-Preserving Numerical Schemes

被引：13

作者：

Bihlo, Alexander ^{[1
]}

Valiquette, Francis ^{[2
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] SUNY Coll New Paltz, Dept Math, 1 Hawk Dr, New Paltz, NY 12561 USA

来源：

SYMMETRIES AND INTEGRABILITY OF DIFFERENCE EQUATIONS | 2017年

基金：

加拿大自然科学与工程研究理事会;

关键词：

DIFFERENCE-SCHEMES; POINT SYMMETRIES; LIE SYMMETRIES; HEAT-TRANSFER; EQUATIONS; DISCRETIZATION; INVARIANTIZATION; INTEGRATION; FRAMES;

D O I：

10.1007/978-3-319-56666-5_6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In these lectures we review two procedures for constructing finite difference numerical schemes that preserve symmetries of differential equations. The first approach is based on Lie's infinitesimal symmetry generators, while the second method uses the novel theory of equivariant moving frames. The advantages of both techniques are discussed and illustrated with the Schwarzian differential equation, the Korteweg-de Vries equation and Burgers' equation. Numerical simulations are presented and innovative techniques for obtaining better invariant numerical schemes are introduced. New research directions and open problems are indicated at the end of these notes.

引用

页码：261 / 324

页数：64