Geometric Foundations of Numerical Algorithms and Symmetry

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.