Volume 25, Issue 4
Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations

Mingzhan Song ,  Xu Qian ,  Hong Zhang ,  Jingmin Xia and Songhe Song


Commun. Comput. Phys., 25 (2019), pp. 1127-1143.

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  • Abstract

In this paper, we mainly propose two kinds of high-accuracy schemes for the coupled nonlinear Schrödinger (CNLS) equations, based on the Fourier pseudospectral method (FPM), the high-order compact method (HOCM) and the Hamiltonian boundary value methods (HBVMs). With periodic boundary conditions, the proposed schemes admit the global energy conservation law and converge with even-order accuracy in time. Numerical results are presented to demonstrate the accuracy, energypreserving and long-time numerical behaviors. Compared with symplectic RungeKutta methods (SRKMs), the proposed schemes are assuredly more effective to preserve energy, which is consistent with our theoretical analysis.

  • History

Published online: 2018-12

  • AMS Subject Headings

37M05, 65M06

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