Numerical methods and nature

Research output: Contribution to journalArticlepeer-review

Abstract

In many numerical procedures one wishes to improve the basic approach either to improve efficiency or else to improve accuracy. Frequently this is based on an analysis of the properties of the discrete system being solved. Using a linear algebra approach one then improves the algorithm. We review methods that instead use a continuous analysis and properties of the differential equation rather than the algebraic system. We shall see that frequently one wishes to develop methods that destroy the physical significance of intermediate results. We present cases where this procedure works and others where it fails. Finally we present the opposite case where the physical intuition can be used to develop improved algorithms.

Original languageEnglish
Pages (from-to)549-570
Number of pages22
JournalJournal of Scientific Computing
Volume28
Issue number2-3
DOIs
StatePublished - Sep 2006

Keywords

  • Finite differences
  • Preconditioning
  • Regularization

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