A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension

AbstractCarroll, J., A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension, Journal of Computational and Applied Mathematics 46 (1993) 327–343.We apply the numerical method of lines to approximate the solution of a system of parabolic partial differential equations in one space dimension. By approximating the spatial derivatives by discrete values of the solution at a set of mesh points in space, we use these approximations to represent the partial differential equations at each mesh point, giving a semidiscrete system of ordinary differential equations in the time direction. The resulting ODE system is integrated numerically using a second-order L-stable composite integration scheme (the author, this journal, 1989) using variable stepsize integration. An implementation of the composite scheme is applied to approximate the solution of some test problems selected from the literature using a uniform spatial mesh. We present the results of a number of numerical experiments which allow an appraisal of the proposed approach with published works