A reduced fourth-order compact difference scheme based on a proper orthogonal decomposition technique for parabolic equations - Baozou Xu; Xiaohua Zhang (Boundary Value Problems, 2019)
Abstract In this paper, we present a reduced high-order compact finite difference scheme for numerical solution of the parabolic equations. CFDS4 is applied to attain high accuracy for numerical solution of parabolic equations, but its computational efficiency still needs to be improved. Our approach combines CFDS4 with proper orthogonal decomposition (POD) technique to improve the computational efficiency of the CFDS4. The validation of the proposed method is demonstrated by four test problems. The numerical solutions are compared with the exact solutions and the solutions obtained by the CFDS4. Compared with CFDS4, it is shown that our method has greatly improved the computational efficiency without a significant loss in accuracy for solving parabolic equations.