求解广义improved KdV方程的守恒差分算法

Conservative Difference Scheme for the General improved KdV Equation

摘要:

本文对广义improved KdV方程的初边值问题进行了数值研究，提出了一个两层非线性有限差分格式，该格式合理地模拟了方程本身具有的两个守恒律。讨论了差分解的存在唯一性，并在其差分解的先验估计的基础上利用能量方法分析了该格式的二阶收敛性与无条件稳定性，数值算例表明本文的格式是可行的。

Abstract:

In this paper, a conservative difference scheme for an initial-boundary value problem of the general improved KdV equation is proposed. This scheme simulates the two conservation properties of the problem well. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, second order convergence and unconditional stability are discussed.Numerical examples show the availability of scheme.