| 高阶紧致差分方法在五次非线性Schrödinger方程中的应用 |
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| 引用本文： | 王普,姜珊珊,肖聪.高阶紧致差分方法在五次非线性Schrödinger方程中的应用[J].北京化工大学学报(自然科学版),2021,48(1):115-118. |
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| 作者姓名： | 王普 姜珊珊 肖聪 |
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| 作者单位： | 北京化工大学 数理学院, 北京 100029 |
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| 摘 要： | 用紧致分裂的思路给出五次非线性Schrödinger方程的一个数值格式，使其收敛阶为O（τ2+h4）。首先在时间上用Strang-type方法将原方程离散分为两个子方程，其中一个有显示解，这样仅对另一个子方程进行高阶差分即可。然后证明此分裂差分格式满足电荷守恒。最后给出数值实验证明格式的收敛阶。
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| 关 键 词： | 非线性Schrödinger方程 紧致差分格式 Strang-type分裂 电荷守恒定律 |
| 收稿时间： | 2020-04-22 |
A high-order compact splitting method for the nonlinear Schrödinger equation with a quintic term |
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| WANG Pu,JIANG ShanShan,XIAO Cong.A high-order compact splitting method for the nonlinear Schrödinger equation with a quintic term[J].Journal of Beijing University of Chemical Technology,2021,48(1):115-118. |
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| Authors: | WANG Pu JIANG ShanShan XIAO Cong |
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| Institution: | College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | An order of O(τ2+h4) different scheme is applied to the nonlinear Schrödinger equation with a quintic term. We first use a Strang-type splitting method to divide the equation into two parts. Only one part needs to be discretized by a high-order compact difference method, because the other part can be solved exactly. The scheme is shown to satisfy the charge conservation law. Some numerical results are given to illustrate the convergence of the scheme. |
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| Keywords: | nonlinear Schrödinger equation compact difference method Strang-type splitting charge conservation law |
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