Generalized Du Fort-Frankel methods for parabolic initial-boundary value problems

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.