Accuracy improvement of a multistep splitting method for nonlinear viscous wave equations

摘要

This paper focuses on a multistep splitting method for a class of nonlinear viscous equations in two spaces, which uses second-order backward differentiation formula (BDF2) combined with approximation factorization for time integration, and second-order centred difference approximation to second derivatives for spatial discretization. By the discrete energy method, it is shown that this splitting method can attain second-order accuracy in both time and space with respect to the discrete L~2- and H~1 -norms. Moreover, for improving computational efficiency, we introduce a Richardson extrapolation method and obtain extrapolation solution of order four in both time and space. Numerical experiments illustrate the accuracy and performance of our algorithms.