SIAM Journal on Numerical Analysis · 2004 · 168 citations · 12 references
Natural SciencesPhysicsComputational PhysicsDifferential EquationsConvergence AnalysisNumerical AlgorithmsNumerical Methods For Differential EquationsRelaxation MethodsSchrödinger EquationVariational FormulationConvergenceDensityEnergy-conserving SchemesNonlinear Schrödinger EquationNonlinear SystemsNumerical Solution Of The Schrödinger EquationRelaxation Theory
In this paper, we present a new numerical scheme for the nonlinear Schrödinger equation. This is a relaxation-type scheme that avoids solving for nonlinear systems and preserves density and energy. We give convergence results for the semidiscretized version of the scheme and perform several numerical experiments.
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