Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems

Axford, R.

Los Alamos National Laboratory

关键词: Numerical Solution;    Differential Equations;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Symmetry;    Construction;   

DOI  :  10.2172/810261
RP-ID  :  LA-13978
RP-ID  :  W-7405-ENG-36
RP-ID  :  810261

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.