Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems
- LANL
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., NM (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 810261
- Report Number(s):
- LA-13978
- Country of Publication:
- United States
- Language:
- English
Similar Records
On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations
Construction of Superconvergent Discretizations with Differential-Difference Invariants