Communications in Computational Physics · 2011 · 19 citations · 33 references
Spectral TheoryNumerical AnalysisMethod Of Fundamental SolutionBoundary ConditionsEngineeringUnbounded Spatial DomainPhysicsFree Boundary ProblemHigh-frequency ApproximationNonlinear Hyperbolic ProblemSchrödinger EquationComputational MechanicsSchrödinger EquationsIntegrable SystemBoundary Element MethodNumerical Method For Partial Differential Equation
Abstract The paper is concerned with the numerical solution of Schrödinger equations on an unbounded spatial domain. High-order absorbing boundary conditions for one-dimensional domain are derived, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate. Then a second order finite difference scheme is proposed, and the convergence of the scheme is established as well. Finally, numerical examples are reported to confirm our error estimates of the numerical methods.
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