Computation of solutions for an overdetermined system of partial difference equations

Abstract

In this paper, we provide an implementable algorithm for computing solutions of a system of linear partial difference equations (pdes) with real constant coefficients having n independent variables and one dependent variable. An important consideration for explicitly solving a system of pdes lies in specifying the initial and/or boundary conditions. We assume that an initial condition set, in the form of a characteristic set, is provided along with the system of pdes. In such a scenario, we provide an algorithm, based on Gröbner basis, which explicitly computes the solution trajectory for the system of pdes at a specified point in the domain. The algorithm can be tested using any standard computer algebra package.