Fully discrete methods for the nonlinear Schrödinger equation

Lee, H.Y.

doi:10.1016/0898-1221(94)00148-0

Cited by 8 publications

(1 citation statement)

References 7 publications

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“…(These conditions are automatically satisfied if d = 1 or the domain is polygonal or in the case of periodic boundary conditions). Lee [96] proved that FEG methods with certain modified IRK methods applied to (2.23) with right hand side f (x, t, u) are of optimal accuracy, and provided numerical results to support the theory.…”

Section: Nonlinear Problemsmentioning

confidence: 79%

Numerical Methods for Schrödinger-Type Problems

Fairweather¹,

Khebchareon²

2002

Applied Optimization

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Several physical phenomena are modeled by initial-boundary value problems which can be formulated as SchrOdinger -type systems of partial differential equations. In this paper, two classes of problems of this kind, Schrodinger equations, which arise in various areas of physics, and certain vibration problems from civil and mechanical engineering, are considered. A survey of numerical methods for solving linear and nonlinear problems in one and several space variables is presented, with special attention being devoted to the parabolic wave equation, the cubic Schrodinger equation, and to fourth order parabolic equations arising in vibrating beam and plate problems. Recently developed finite element methods for solving SchrOdinger-type systems are also outlined.Keywords: Schrodinger systems, linear and nonlinear Schrodinger equations, parabolic wave equation, vibrating beams and plates, fourth order parabolic equations, finite difference methods, finite element Galerkin methods, orthogonal spline collocation methods, spectral methods IntroductionWe consider the numerical solution of problems that can be written as initialboundary value problems (IBVPs) for real systems of partial differential equations of the form

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Section: Nonlinear Problemsmentioning

confidence: 79%