2维Ginzburg-Landau方程的分裂LOD高阶紧致格式

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

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.