A linearlized mass-conservative fourth-order block-centered finite difference method for the semilinear Sobolev equation with variable coefficients

Abstract

In this paper, a two-dimensional variable-coefficients semilinear Sobolev equation under Neumann boundary condition is considered, and a novel Crank–Nicolson type linearized fourth-order block-centered finite difference scheme which preserves mass is developed and analyzed. Under local Lipschitz continuous assumption on the nonlinear source term, second-order temporal and fourth-order spatial accuracy are rigorously proved for the primal scalar variable p, its gradient u and its flux q simultaneously. Then, stability under a rough time stepsize condition is proved following the convergence results. Numerical experiments are presented to confirm the theoretical conclusions and well performance of the proposed scheme.