2维Ginzburg-Landau方程的分裂LOD高阶紧致格式  

The Splitting High-Order Compact Scheme for Two-Dimensional Ginzburg-Landau Equation

作　　者：匡立群 孔令华[1] 王兰[1] 郑小红[2] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022 [2]广东农工商职业技术学院基础部,广东广州510507

出　　处：《江西师范大学学报（自然科学版）》2017年第1期35-38,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11301234;11271171);江西省自然科学基金(20142BCB23009;20161ACB20006)资助项目

摘　　要：采用分裂技巧研究了2维的Ginzburg-Landau方程构造高效的数值格式.把2维Ginzburg-Landau方程变成线性和非线性问题以避免求解耦合的非线性方程组.为减少存储量和计算量,对线性问题进一步运用局部1维方法,把它分解为2个1维问题求解.所得到的数值格式具有高效、高精度等数值特征.最后,用数值算例模拟了2维Ginzburg-Landau方程所描述的物理现象,新方法具有较大的优越性.The efficient numerical scheme for two-dimensional Ginzburg-Landau equation is studied by splitting method. The two-dimensional Ginzburg-Landau equation is altered into a linear problem and a nonlinear problem in order to avoid solving a coupled nonlinear algebraic system. In order to reduce storage and computation,the linear problem can be decomposed into two one dimensional problems by local one-dimensional method. The scheme has the numerical characteristics such as high efficiency,high accuracy. Finally,some numerical experiments are reported to simulate the physical phenomena described by two-dimensional Ginzburg-Landau equation,and the superiority of our scheme can be verified by the experiments.

关 键 词：GINZBURG-LANDAU方程 分裂法 局部1维法 高阶紧致格式 

分 类 号：O241.82[理学—计算数学]