Chen Jiaqi, Dai Weizhong
Mathematics Department, University of California, Santa Cruz, CA 95060, United States.
Mathematics & Statistics, College of Engineering & Science, Louisiana Tech University, Ruston, LA 71272, United States.
MethodsX. 2023 Jan 21;10:102036. doi: 10.1016/j.mex.2023.102036. eCollection 2023.
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.
研究在长通道一端作用有周期力的Korteweg-de Vries（KdV）型方程的长时间解的行为，对于模拟由心脏脉冲驱动的动脉中的血流非常重要。开发一种精确的数值方法来求解强迫KdV问题具有很大的意义。在本文中，我们提出了以下方法来获得KdV问题解的精确近似。
• 提出了一种精确的紧致有限差分格式，用于求解上述具有四阶精度的强迫KdV问题。
• 在区间右端使用吸收边界条件来避免波的反射。
• 通过冯·诺依曼方法证明了格式的稳定性，然后通过三个例子进行了测试。结果表明，该方法提供了精确的解，并且波传播时没有反射。
