A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation

Abstract This paper focuses on developing the reduced-order extrapolated model based on the splitting implicit finite difference (SIFD) scheme and the proper orthogonal decomposition (POD) for the two-dimensional (2D) fourth-order nonlinear Rosenau equation. For this purpose, we first construct the SIFD scheme and analyze the stability and convergence. And then, we develop a reduced-order extrapolated SIFD (ROESIFD) scheme for the Rosenau equation by POD technique and analyze the ability and convergence for the ROESIFD solutions. Finally, we enumerate an example to illustrate the efficacy and feasibility of the ROESIFD scheme.