Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems
New methods are developed to construct exact difference equations from which numerical solutions of both initial value problems and two-point boundary value problems involving first and second order ordinary differential equations can be computed. These methods are based upon the transformation theory of differential equations and require the identification of symmetry properties of the differential equations. The concept of the divergence-invariance of a variational principle is also applied to the construction of difference equations. It is shown how first and second order ordinary differential equations that admit groups of point transformations can be integrated numerically by constructing any number of exact difference equations.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 810261
- Report Number(s):
- LA-13978; TRN: US200309%%183
- Resource Relation:
- Other Information: PBD: 2 Aug 2002
- Country of Publication:
- United States
- Language:
- English
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