摘要
其中i=(-1)(1/2),△为Laplace算子,q(·)为实变量实值函数,u_0(x)和u(x,t)分别为关于x以2π为周期的已知和未知复值函数,J=(0,T](T>0),β为一实常数,e_j为R^m的第j个单位向量,x=(x_1,…,x_m)∈R^m. 方程(1.1)在非线性光学、等离子体物理。
Fourier spectral methods of Galerkin and collocation type for multi-dimensional andnonlinear Schrodinger equations are presented. Convergence with spectral accuracy is provedfor both Galerkin and collocation approximations. Stable discretizations in time by one-stepand two-step methods are analyzed. An algorithm for the discretizations is proposed. The nu-mber of operations for the pseudo-spectral technique by FFT is computed. Finally, some nu-merical results are given, which are compared with those of other methods.
出处
《计算数学》
CSCD
北大核心
1991年第1期25-33,共9页
Mathematica Numerica Sinica
基金
陕西师范大学青年科学基金
