| 时间分数阶薛定谔方程的数值方法 |
| |
| 引用本文： | 张艳敏,张丽春.时间分数阶薛定谔方程的数值方法[J].北华大学学报(自然科学版),2014,0(3):296-298. |
| |
| 作者姓名： | 张艳敏 张丽春 |
| |
| 作者单位： | 青岛理工大学琴岛学院,山东 青岛,266106;北华大学数学与统计学院,吉林 吉林,132033 |
| |
| 基金项目： | 国家自然科学基金项目(项目编号：11271101) |
| |
| 摘 要： | 结合非标准有限差分格式给出了求解分数阶薛定谔方程的一种数值解法,对时间导数离散后的分母构造了一个关于时间步长的函数来近似,证明了该差分格式是无条件收敛和稳定的.数值算例表明该方法不仅有非常好的收敛性和稳定性,还有较高的精度,因此该方法是有效的.
|
| 关 键 词： | 分数阶薛定谔方程 非标准有限差分格式 无条件收敛 无条件稳定 |
A Numerical Method for Solving Time Fractional Schrodinger Equation |
| |
| ZHANG Yan-min,ZHANG Li-chun.A Numerical Method for Solving Time Fractional Schrodinger Equation[J].Journal of Beihua University(Natural Science),2014,0(3):296-298. |
| |
| Authors: | ZHANG Yan-min ZHANG Li-chun |
| |
| Institution: | 1. Qindao College of Qingdao Technological University, Qingdao 266106, China ; 2. Mathematics and Statistics School of Beihua University, Jilin 132033, China ) |
| |
| Abstract: | Combined the nonstandard finite difference schemes, a numerical method for solving the time fractional Schrodinger equation has been presented,denominator function for the space discrete derivatives is a space step function, and the difference scheme is unconditional stability and convergence. Numerical example shows that the numerical method has not only good convergence and stability, but also higher precision. So the numerical method is a practical method. |
| |
| Keywords: | fractional Schrodinger equation nonstandard finite difference schemes unconditional convergence unconditional stability |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
