Automatic generation of finite difference equations and fourier stability analyses

Abstract

Recently several software tools based on the algebraic manipulation system MACSYMA have been implemented which facilitate the design, analysis and construction of finite difference programs for the numerical solution of systems of partial differential equations. Two of them are described here. The FDIFF package converts scalar, non-linear partial differential equations into linear, finite difference approximations. It includes tools for discretization of the domain of the PDE's dependent variables, linearization of non-linear terms and conversion of derivative terms into finite difference expressions. A notation and algebra for building arbitrary finite difference operators is provided. The FSTAB package automatically performs local Fourier stability analyses on sets of finite difference equations by deriving amplification matrices.