A compact finite difference scheme with absorbing boundary condition for forced KdV equation

Jiaqi Chen; Weizhong Dai

doi:10.1016/j.mex.2023.102036

A compact finite difference scheme with absorbing boundary condition for forced KdV equation

MethodsX. 2023 Jan 21:10:102036. doi: 10.1016/j.mex.2023.102036. eCollection 2023.

Authors

Jiaqi Chen¹, Weizhong Dai²

Affiliations

¹ Mathematics Department, University of California, Santa Cruz, CA 95060, United States.
² Mathematics & Statistics, College of Engineering & Science, Louisiana Tech University, Ruston, LA 71272, United States.

Abstract

Studying the long-time solution behavior of the Korteweg-de Vries (KdV) type equation with a periodic force acting at one end of the long channel is important for simulating the blood flow in artery driven by heart pulses. It is of great interest to develop an accurate numerical method for solving the forced KdV problem. In this article, we present the following methods to obtain an accurate approximation to the solution of KdV problem.•An accurate compact finite difference scheme is proposed for solving the above forced KdV problem with fourth-order accuracy.•An absorbing boundary condition at the right end of the interval is used to avoid the wave reflection.•The stability of scheme is proved by the von Neumann method and then tested by three examples. Results show that the method provides an accurate solution, and the wave propagates without reflection.

Keywords: Absorbing boundary condition; Compact Finite Difference Scheme; Compact difference scheme; KdV equation.