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 language | English (US) |
|---|---|
| Pages (from-to) | 417-436 |
| Number of pages | 20 |
| Journal | Applicable Algebra in Engineering, Communications and Computing |
| Volume | 11 |
| Issue number | 5 |
| DOIs | |
| State | Published - Apr 2001 |
Keywords
- Differential invariant
- Divided difference
- Geometric integration
- Jet
- Joint invariant
- Lie group
- Moving frame
- Multi-space