Kdv浅水波方程的Crank-Nicolson差分格式

摘要

The numerical solution of nonlinear evolution equations is important. Among the nonlinear evolution equations, Kdv shallow water wave equation is the most typical representative of nonlinear dispersive wave equation. In this paper, Crank-Nicolson finite difference method having good stability and second order convergence was used for solving Kdv shallow water wave equation fixed-solutions. The physical phenomenon of solitary waves can be simulated numerically. So the difference method is effective.%对非线性发展方程数值求解有着重要意义,而非线性发展方程中,Kdv浅水波方程是最典型的非线性色散波动方程的代表.针对Kdv浅水波方程的定解问题,用Crank-Nicolson差分法求解,该法具有良好的稳定性及二阶收敛性,并能数值模拟出孤立波这一物理现象,说明该差分格式是有效的.