A Stable Explicit Scheme for Solving Inhomogeneous Constant Coefficients Differential Equation using Green's Function

A numerical explicit method to evaluates transient solutions of linear partial differential inhomogeneous equation with constant coefficients is proposed. A general form of the scheme for a specific linear inhomogeneous equation is shown. The method is applied to the wave equation and the diffuse equation and is investigated by simulating simple models. The numerical solutions of the proposed method show good agreement to the exact solutions. Comparing with explicit FDM, FDM shows the instability by the violation of CFL condition whereas the proposed method is always stable irrespective of any time step width.