广义sine-Gordon方程高精度隐式紧致差分方法  

A HIGH ACCURACY IMPLICIT COMPACT DIFFERENCE METHOD FOR SOLVING THE GENERALIZED SINE-GORDON EQUATION

作　　者：耿晓月 刘小华[1] 

机构地区：[1]西南石油大学理学院,成都637001

出　　处：《计算数学》2015年第2期199-212,共14页Mathematica Numerica Sinica

摘　　要：本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.For solving two-dimensional nonlinear generalized sine-Gordon（SO） equations, we estab-lished a three-level high order compact alternating direction implicit scheme. Applying the energy analysis method, we obtain that the scheme is convergent to be fourth-order spatial accuracy and second-order temporal accuracy. An implemental Richardson extrapolation method is developed to improve temporal accuracy. The numerical results are provided to verify the algorithm has ability to reach fourth-order accuracy in both time and space.

关 键 词：SG方程 紧致差分格式 交替方向隐格式 外推法 能量分析法 

分 类 号：O241.8[理学—计算数学]