耗散SRLW方程的拟紧致非线性有限差分逼近

Pseudo-compact nonlinear finite difference approximate solution for dissipative symmetric regularized long wave equation

本文对具有耗散项的对称正则长波(SRLW)方程的初边值问题进行了数值研究,提出了一个两层隐式拟紧致差分格式,该格式合理地模拟了问题本身的两个守恒律,得到了差分解的存在唯一性,并在差分解的先验估计的基础上用能量方法分析了该格式的二阶收敛性与无条件稳定性.数值结果表明该格式的精度明显优于一般的二阶格式.

An implicit pseudo-compact two-level scheme sipative symmetric regularized long wave equation. The is proposed for the initial value problems of dis- scheme simulates two conservation properties of the problem well. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, seeond order convergence and uneonditionally stability are diseussed. Numerical examples show that the aceuracy of the scheme is much better than the general second order scheme.