The stability of the Du Fort-Frankel method for the diffusion equation with boundary conditions involving space derivatives

Abstract

It is shown that the Du Fort-Frankel method is unstable for the diffusion equation, if the usual central difference approximations are made to linear boundary conditions involving first order space derivatives. This is shown to be true even when the corresponding differential equation is stable. A modified boundary condition is presented which is proved to be stable provided the differential equation is stable.