| 摘要: |
| 本文对五次非线性 方程提出了一个四阶紧致有限差分格式，证明格式在离散意义下保持原问题的两个守恒性质，即质量守恒和能量守恒.引入“抬升”技巧，运用标准的能量方法和数学归纳法建立了误差的最优估计，证明数值解在空间和时间两个方向分别具有四阶和二阶精度.数值实验对理论结果进行了验证，并与已有结果进行了对比，结果表明本文格式在保持精度相当的前提下具有更高的计算效率. |
| 关键词: 五次NLS方程；紧有限差分格式；守恒律 最优误差估计；计算效率 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| A new compact finite difference scheme for the quantic nonlinear Schrödinger equation |
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xuexiang, wangtingchun
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Nanjing University of Information Science and Technology
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| Abstract: |
| In this paper, we propose a fourth-order compact finite difference scheme for the nonlinear Schr?dinger equation with a quintic term. We prove that the scheme preserves the total mass and energy, respectively. By introducing the lifting technique, the optimal error estimate of the proposed scheme is established by using the standard energy method and the mathematical induction. It is proved that the numerical solution has accuracy of fourth order and second order, respectively, in space and time. Numerical experiments are given to verify the theoretical results and compared with the existing results. The results show that the proposed scheme is of higher computational efficiency under the condition of maintaining high accuracy. |
| Key words: Quintic NLS equation Compact finite difference scheme Conservation laws Optimal error estimate Computational efficiency. |
