KdV方程的几类数值方法比较

发布时间：2018-05-23 15:18

本文选题：KdV方程 + 有限差分法　；参考：《湘潭大学》2017年硕士论文

【摘要】：本文针对Korteweg-de Vries (KdV)方程,在空间上考虑用有限差分法、DDG方法、LDG方法离散,对时间主要采用Crank-Nicolson方法离散。文中给出了这几种方法的半离散及全离散格式,并列出了每种格式满足的守恒律。通过几个典型的数值算例,从收敛性、稳定性以及满足方程的守恒特征等方面考察这几种方法的数值表现,数值结果表明,DDG与LDG优于有限差分方法。
[Abstract]:In this paper, for the Korteweg-de Vries KDV) equation, the finite difference method is considered to be used to discretize the Korteweg-de Vries equation, and the Crank-Nicolson method is mainly used to discretize the time. In this paper, the semi-discrete and fully discrete schemes of these methods are given, and the conservation laws satisfied by each scheme are listed. Through several typical numerical examples, the numerical performances of these methods are investigated from the aspects of convergence, stability and conserved characteristic of the equation. The numerical results show that LDG and DG are superior to the finite difference method.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8

【参考文献】