Uniformly accurate nested Picard iterative schemes for nonlinear Schrödinger equation with highly oscillatory potential

Li, Jiyong

doi:10.1016/j.apnum.2023.06.005

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“…2 of 27 the energy or other invariants (see, e.g., [52][53][54][55][56][57][58][59][60][61]) have been investigated: the methods we shall deal with, are exactly placed in this latter setting. The basic approach follows what suggested in [62, page 187], namely by suitably using the method of lines: if the PDEs are of Hamiltonian type, [.…”

Section: Introductionmentioning

confidence: 99%

Recent Advances in the Numerical Solution of the Nonlinear Schrödinger Equation

Barletti,

Brugnano,

Gurioli

et al. 2023

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In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space-time accuracy.

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