High-order compact difference schemes with Richardson extrapolation for semilinear parabolic systems

Abstract

We propose sixth-order approximations for semilinear parabolic systems that are based on fourth-order compact difference schemes combined with Richardson extrapolation. Within this paper, Richardson extrapolation is applied directly to the solution procedures used within existing numerical algorithms for realization of compact fourth-order difference schemes. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed finite difference discretization strategy.