Geometric Foundations of Numerical Algorithms and Symmetry | Zendy

Peter J. Olver | Zendy

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Geometric Foundations of Numerical Algorithms and Symmetry

Author(s) -

Peter J. Olver

Publication year - 2001

Publication title -

applicable algebra in engineering communication and computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.558

H-Index - 35

eISSN - 1432-0622

pISSN - 0938-1279

DOI - 10.1007/s002000000053

Subject(s) - analogy , geometric analysis , mathematics , invariant (physics) , symmetry (geometry) , differential equation , differential (mechanical device) , differential geometry , space (punctuation) , numerical analysis , algorithm , algebra over a field , computer science , mathematical analysis , geometry , ordinary differential equation , differential algebraic equation , pure mathematics , physics , mathematical physics , philosophy , linguistics , thermodynamics , operating system

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

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