A FINITE-DIFFERENCE METHOD FOR SYMMETRICAL POSITIVE DIFFERENTIAL-EQUATIONS

Abstract

A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of O(h(1/2)), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backward heat equations.