耦合微分的緊緻數值方法解一階KDV方程

Abstract

這篇論文主要之目的是使用耦合微分的緊緻數值方法來解一階KDV方程。首先，我們先回顧一階和二階耦合微分的緊緻數值方法。接著，我們會學習一階和三階耦合微分的緊緻數值方法。再來，我們簡要地介紹Runge-Kutta Methods。最後，我們會給一些例子並且列出數值結果，然後做出結論。

The primary objective of this thesis is to use coupled derivatives compact schemes (CD) for solving one-dimensional KDV equation. First, we review the coupled first and second derivatives scheme and then we study the coupled first and third derivatives scheme. Next, we introduce roughly the Runge-Kutta methods. Finally, we give some examples and show numerical results, and the conclusion follows.