A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

A monotone compact implicit finite difference scheme with fourth-order accuracy inspace and second-order in time is proposed for solving nonlinear reaction-diffusion equations.An accelerated monotone iterative method for the resulting discrete problem ispresented.The sequence of iteration converges monotonically to the unique solution ofthe discrete problem,and the convergence rate is either quadratic or nearly quadratic,depending on the property of the nonlinear reaction.The numerical results illustrate thehigh accuracy of the proposed scheme and the rapid convergence rate of the iteration.