A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation

In this study, we devote ourselves to the reduced-order extrapolated finite difference iterative (ROEFDI) modeling and analysis for the two-dimensional (2D) Sobolev equation. To this end, we first establish the reduced-order extrapolated finite difference iterative (ROEFDI) scheme holding sufficiently high accuracy but containing very few degrees of freedom for the 2D Sobolev equation via the proper orthogonal decomposition (POD) technique. And then, we analyze the stability and convergence of the ROEFDI solutions. Finally, we use the numerical experiments to verify the feasibility and effectiveness of the ROEFDI scheme.