In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference space-time method. The KdV and RLW equations are partial differential equations that describe the behavior of long shallow water waves. We show that the finite difference space-time method is an effective way to solve these equations numerically, and we compare the results with those obtained using explicit method and generalized finite difference (GFD) formulae. Our results indicate that the finite difference space-time method provides accurate and stable solutions for both the KdV and RLW equations.

在本文中，我们使用有限差分时空方法对 Korteweg-de Vries (KdV) 和正则化长波 (RLW) 方程进行了数值分析。KdV 和 RLW 方程是描述长浅水波行为的偏微分方程。我们证明了时空有限差分法是数值求解这些方程的有效方法，并将结果与​​使用显式方法和广义有限差分（GFD）公式获得的结果进行了比较。我们的结果表明，有限差分时空法为 KdV 和 RLW 方程提供了准确且稳定的解。