Optimized integrating factor technique for Schrödinger-like equations

Lovisetto, Martino; Clamond, Didier; Marcos, Bruno

doi:10.1016/j.apnum.2022.04.011

Cited by 2 publications

(2 citation statements)

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“…The freedom provided by the gauge condition of the potential is exploited to compute an optimal value of C n , which allows to choose a larger time-step compared to the C n = 0 case and therefore speeding up the numerical integration. The resulting optimal value, Cn , which is obtained at each time step n as the value of C n minimising the L 2 -norm of N [30], is…”

Section: Discussionmentioning

confidence: 99%

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Integrating factor techniques applied to the Schrödinger-like equations. Comparison with Split-Step methods

Lovisetto¹,

Clamond²,

Marcos³

2022

Preprint

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The nonlinear Schrödinger and the Schrödinger-Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to numerically solve these equations) and the integrating factor technique, also called Lawson method. Indeed, the latter is known to perform very well for the nonlinear Schrödinger equation, but has not been thoroughly investigated for the Schrödinger-Newton equation. Comparisons are made in one and two spatial dimensions, exploring different boundary conditions and parameters values. We show that for the short range potential of the nonlinear Schrödinger equation, the integrating factor technique performs better than splitting algorithms, while, for the long range potential of the Schrödinger-Newton equation, it depends on the particular system considered.

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Section: Discussionmentioning

confidence: 99%

“…Here, we focus on adaptive Runge-Kutta methods [27,29]. As explained in [30], it is possible to further improve and optimize the integrating factor method. The details of this improved version of the integrating factor technique are illustrated in Appendix A.…”

Section: Integrating Factormentioning

confidence: 99%