Geometric foundations of numerical algorithms and symmetry

Peter J. Olver

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

This paper outlines a new general construction, named "multi-space", that forms the proper geometrical foundation for the numerical analysis of differential equations - in direct analogy with the role played by jet space as the basic object underlying the geometry of differential equations. Application of the theory of moving frames leads to a general framework for constructing symmetry-preserving numerical approximations to differential invariants and invariant differential equations.

Original languageEnglish (US)
Pages (from-to)417-436
Number of pages20
JournalApplicable Algebra in Engineering, Communications and Computing
Volume11
Issue number5
DOIs
StatePublished - Apr 2001

Keywords

  • Differential invariant
  • Divided difference
  • Geometric integration
  • Jet
  • Joint invariant
  • Lie group
  • Moving frame
  • Multi-space

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