4.6 Article

High-Order Linearly Implicit Structure-Preserving Exponential Integrators for the Nonlinear Schrodinger Equation

期刊

JOURNAL OF SCIENTIFIC COMPUTING
卷 90, 期 1, 页码 -

出版社

SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-021-01739-x

关键词

SAV approach; Energy-preserving; Integrating factor Runge-Kutta method; Linearly implicit; Nonlinear Schrodinger equation

资金

  1. National Natural Science Foundation of China [11901513, 11971481, 12071481]
  2. National Key R&D Program of China [2020YFA0709800]
  3. Natural Science Foundation of Hunan [2021JJ40655, 2021JJ20053]
  4. Yunnan Fundamental Research Projects [202101AT070208, 202001AT070066, 202101AS070044]
  5. High Level Talents Research Foundation Project of Nanjing Vocational College of Information Technology [YB20200906]
  6. Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems [202102]

向作者/读者索取更多资源

A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schrodinger equation. The methods reformulate the original equation into an equivalent form that satisfies a quadratic energy and apply the Fourier pseudo-spectral method to approximate the spatial derivatives. The proposed schemes produce numerical solutions that precisely conserve the modified energy and are more efficient compared to other existing structure-preserving schemes.
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schrodinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation is first reformulated into an equivalent form which satisfies a quadratic energy. The spatial derivatives of the system are then approximated with the standard Fourier pseudo-spectral method. Subsequently, we apply the extrapolation technique/prediction-correction strategy to the nonlinear terms of the semi-discretized system and a linearized energy-conserving system is obtained. A fully discrete scheme is gained by further using the integrating factor Runge-Kutta method to the resulting system. We show that, under certain circumstances for the coefficients of a Runge-Kutta method, the proposed scheme can produce numerical solutions along which the modified energy is precisely conserved, as is the case with the analytical solution and is extremely efficient in the sense that only linear equations with constant coefficients need to be solved at every time step. Numerical results are addressed to demonstrate the remarkable superiority of the proposed schemes in comparison with other existing structure-preserving schemes.

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