A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients

Mehdi Dehghan; Ameneh Taleei

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A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients

机译：求解具有常数和可变系数的非线性Schrodinger方程的紧凑式分步有限差分方法

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摘要

We propose a compact split-step finite difference method to solve the nonlinear Schrodinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and Gross–Pitaevskii equation.

机译：我们提出了一种紧凑的分步有限差分方法来求解具有恒定系数和可变系数的非线性Schrodinger方程。该方法通过引入紧凑的空间变量离散方案来提高分步有限差分法的精度，而这种改进不会减小稳定性范围，也不会增加计算成本。此方法还保留了一些守恒定律。通过使用具有常数和可变系数的立方非线性Schrodinger方程以及Gross-Pitaevskii方程，进行了数值测试，以验证新数值方法的理论结果。

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《Computer physics communications》 |2010年第1期|共9页
作者
Mehdi Dehghan; Ameneh Taleei;
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正文语种 eng
中图分类计算机的应用;
关键词
Nonlinear Schrodinger equation (NLS); Gross–Pitaevskii equation (GP); Operator splitting; Compact split-step finite difference method; (SSFD);

机译：非线性Schrodinger方程（NLS）;Gross–Pitaevskii方程（GP）;算子分裂;紧凑的分步有限差分法;（SSFD）;

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专利

1. A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients [J] . Mehdi Dehghan, Ameneh Taleei Computer physics communications . 2010,第1期

机译：求解具有常数和可变系数的非线性Schrodinger方程的紧凑式分步有限差分方法
2. An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations [J] . Wang Nan, Huang Chengming Computers & mathematics with applications . 2018,第7期

机译：非线性分数阶Ginzburg-Landau方程组的高效分步拟紧凑有限差分方法
3. Instability of the finite-difference split-step method applied to the generalized nonlinear Schrodinger equation. III. external potential and oscillating pulse solutions [J] . Lakoba Taras I. Numerical Methods for Partial Differential Equations: An International Journal . 2017,第3期

机译：有限差分分裂步骤方法应用于广义非线性薛定林方程的稳定性。 III。外部电位和振荡脉冲解决方案
4. Solving coupled nonlinear Schrodinger equations using cubic B-spline interpolation and finite difference methods [C] . Hanis Safirah Saiful Anuar, Amirah Azmi, Nur Nadiah Abd Hamid, National Symposium on Mathematical Sciences . 2017

机译：立方B样条插值求解耦合非线性Schrodinger方程及有限差分方法
5. On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients. [D] . Luo, Jun. 2007

机译：具有常数系数的抛物线型Bellman方程的有限差分近似的收敛速度。
6. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals [O] . Hector Vazquez-Leal, Brahim Benhammouda, Uriel Antonio Filobello-Nino, -1

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7. A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients [O] . Hejazi Hala, Moroney Tim, Liu Fawang 2013

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A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients

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