摘要
为剖析变系数分数阶薛定谔方程的有限差分数值方法.利用包括分数阶中心差分公式和Taylor展开式等相关理论,构造了求解变系数分数阶薛定谔方程的三层线性化差分格式,然后对差分格式的截断误差进行分析.最后,借助于几个具体的数值算例对差分格式的有效性进行了验证.结果表明,变系数分数阶薛定谔方程的数值算例结果的误差均很小,说明该差分格式是有效的.时间系数对于差分格式的有效性无直接影响.
In order to analyze the finite difference numerical method of variable coefficient fractional Schr dinger equation,a three-layer linearized difference scheme for solving the variable coefficient fractional Schr dinger equation is constructed using relevant theories such as the fractional order central difference formula and Taylor expansion.Then the truncation error of the difference scheme is analyzed.Finally,several specific numerical examples are used to verify the effectiveness of the difference scheme.The results show that the numerical examples of the variable coefficient fractional Schr dinger equation have very small errors,indicating that the difference scheme is effective.The time coefficient has no direct impact on the effectiveness of the difference scheme.
作者
沈欢欢
SHEN Huanhuan(Basic Department,Chuzhou City Vocational College,Chuzhou Anhui 239000)
出处
《宁夏师范学院学报》
2023年第4期27-34,共8页
Journal of Ningxia Normal University
基金
滁州城市职业学院科研项目(2019SK02).
关键词
非线性薛定谔方程
线性化差分
变系数
有效性
Nonlinear Schr dinger equation
Linearized difference
Variable coefficient
Validity
