摘要
研究了一类四阶非线性耗散、色散波动方程初边值问题的有限差分解法。对求解方程构造了一个三层隐式差分格式,消除了显格式的稳定性对计算步长的严格限制,使之适用范围更广,并用能量估计的方法严格证明了差分格式的收敛性与稳定性,该格式对于时间和空间均具有二阶收敛性。最后给出了一些数值结果,验证了理论分析的正确性。
This paper considers the finite difference method for a class of generalized fourth order dispersive and dissipative wave equation. In order to get the numerical solution, the paper devises a three hierarchic implicit scheme which eliminates the strict restriction of explicit scheme, thus, it can be used in more areas. By using the energy estimation method, the convergence and stability of the difference scheme are proved and the scheme is second order convergence for time and space. In the last, some numerical results are presented to validate the correctness of the theoretic analysis.
出处
《山东科技大学学报（自然科学版）》
CAS
2007年第4期88-91,共4页
Journal of Shandong University of Science and Technology(Natural Science)
关键词
四阶波动方程
差分法
收敛性
稳定性
fourth order wave equation
difference method
convergence
stability
