求解非线性薛定谔方程的一类数值解法

Numerical Method for Solving Nonlinear Schrodinger Equation

利用非标准有限差分方法构造了求解非线性薛定谔方程的两个非标准有限差分格式。对于离散后的差分格式,把关于时间和空间的步长函数作为分母逼近导数项。对于非线性项,通过非局部的离散方法计算了这两个非标准有限差分格式的局部截断误差。数值实验结果验证了非标准有限差分格式的有效性。

Two nonstandard finite difference schemes for solving the nonlinear Schrodinger equation were constructed by using the nonstandard finite difference method.For discrete difference schemes,the step-size function of time and space was taken as the denominator approximation derivative term.For the non-linear terms,the local truncation errors of these two non-standard finite difference schemes were calculated by non local discrete mode.The numerical results verified the effectiveness of the nonstandard finite difference scheme.