A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations

• The reduced-order extrapolating FD schemes are just developed by Luo’s research team Since 2013 (see [47], [48], [49], [50], [51] and [52]) and a very new technique.
• The reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations is first built by us.
• We provide theoretical analysis and examples to show the advantage of our method.

This paper is concerned with establishing the reduced-order extrapolation central difference (ROECD) scheme based on proper orthogonal decomposition (POD) for two-dimensional (2D) fourth-order hyperbolic equations. For this purpose, we first develop the classical central difference (CD) scheme for the 2D fourth-order hyperbolic equations and analyze its stability and convergence. Then by making use of the POD method, we build the ROECD scheme with fewer degrees of freedom and sufficiently high accuracy and furnish the error estimates of the ROECD solutions and the algorithm procedure for solving the ROECD scheme. Finally, we employ some numerical examples to confirm the correctness of theoretical conclusions. This implies that ROECD scheme is feasible and efficient for seeking the numerical solutions of the 2D fourth-order hyperbolic equations.