TY - JOUR
T1 - Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations
JO - Communications in Computational Physics
VL - 4
SP - 1127
EP - 1143
PY - 2018
DA - 2018/12
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0212
UR - https://global-sci.org/intro/article_detail/cicp/12893.html
KW - Hamiltonian boundary value methods, Fourier pseudospectral method, high-order compact method, coupled nonlinear Schrödinger equations.
AB - <p style="text-align: justify;">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, energy-preserving and long-time numerical behaviors. Compared with symplectic Runge-Kutta methods (SRKMs), the proposed schemes are assuredly more effective to preserve energy, which is consistent with our theoretical analysis.</p>