Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
Journal of Computational Physics
Numerical methods for the generalized Zakharov system
Journal of Computational Physics
An efficient and stable numerical method for the Maxwell-Dirac system
Journal of Computational Physics
Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations
Journal of Computational Physics
An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential
Journal of Computational and Applied Mathematics
Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing NLSs in two dimensions with a linear, cubic, or quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter ${\delta}$ is larger than a threshold value ${\delta}_{\rm th}$. We note that our method can also be applied to solve the three-dimensional Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).