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

Chris J Budd, M D Piggott

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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 Schrödinger equation.
Original languageEnglish
Pages (from-to)399-422
Number of pages24
JournalJournal of Computational and Applied Mathematics
Volume128
Issue number1-2
DOIs
Publication statusPublished - 1 Mar 2001

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