A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation

Xiaohua Zhang and Ping Zhang

Applied Mathematics and Computation, 2018, vol. 339, issue C, 535-545

Abstract: In this paper, a reduced implicit sixth-order compact finite difference (CFD6) scheme which combines proper orthogonal decomposition (POD) technique and high-order compact finite difference scheme is presented for numerical solution of the Korteweg-de Vries (KdV) equation. High-order compact finite difference scheme is applied to attain high accuracy for KdV equation and the POD technique is used to improve the computational efficiency of the high-order compact finite difference scheme. This method is validated by considering the simulation of five examples, and the numerical results demonstrate that the reduced sixth-order compact finite difference (R-CFD6) scheme can largely improve the computational efficiency without a significant loss in accuracy for solving KdV equation.

Keywords: High-order compact finite difference scheme; Proper orthogonal decomposition; KdV equation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:535-545

DOI: 10.1016/j.amc.2018.07.017

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