An Extended Finite Differences Method for the Solution of System Problems

摘要

The material presented here is intended to extend the two hundred year old direct variational method of finite differences (DVMFD) as a numerical integration method for solving differential system equations. A numerical predictor and subsequent idealized numerical integrator are formulated. An existing counterpart to the DVMFD, the action functional, also emerges to provide a direct link between the DVMFD and the principle of Lagrange. A parallel objective then becomes one of exploring the physical identity of the action functional by way of providing an even more generalized Lagrangian recipe for handling a broad class of physical systems. (Author)