A new scheme for the solution of reaction diffusion and wave propagation problems

Abstract

In this paper, a robust numerical scheme is presented for the reaction diffusion and wave propagation problems. The present method is rather simple and straightforward. The Houbolt method is applied so as to convert both types of partial differential equations into an equivalent system of modified Helmholtz equations. The method of fundamental solutions is then combined with the method of particular solution to solve these new systems of equations. Next, based on the exponential decay of the fundamental solution to the modified Helmholtz equation, the dense matrix is converted into an equivalent sparse matrix. Finally, verification studies on the sensitivity of the method’s accuracy on the degree of sparseness and on the time step magnitude of the Houbolt method are carried out for four benchmark problems.