The geometric integration of scale-invariant ordinary and partial differential equations

被引：20

作者：

Budd, CJ ^{[1
]}

Piggott, MD ^{[1
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 128卷 / 1-2期

关键词：

mesh adaption; self-similar solution; scaling invariance; conservation laws; maximum principles; equidistribution;

D O I：

10.1016/S0377-0427(00)00521-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This review paper examines a synthesis of adaptive mesh methods with the use of symmetry to solve ordinary and partial differential equations. It looks at the effectiveness of numerical methods in preserving geometric structures of the underlying equations such as scaling invariance, conservation laws and solution orderings. Studies are made of a series of examples including the porous medium equation and the nonlinear Schrodinger equation. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：399 / 422

页数：24

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