Fully discrete methods for the nonlinear Schrödinger equation

DOI10.1016/0898-1221(94)00148-0zbMath0808.65133OpenAlexW2052012065MaRDI QIDQ1336878

V. Pereyra

Publication date: 6 November 1994

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(94)00148-0

zbMATH Keywords

performanceconvergencenumerical experimentsnonlinear Schrödinger equationRunge-Kutta methodperiodic boundary conditionsfully discrete methodGalerkin-finite element method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (6)

Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation ⋮ Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method ⋮ Superconvergence analysis of finite element method for the time-dependent Schrödinger equation ⋮ On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation ⋮ Superconvergence analysis of bi-\(k\)-degree rectangular elements for two-dimensional time-dependent Schrödinger equation ⋮ Rational methods with optimal order of convergence for partial differential equations

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Galerkin/Runge–Kutta Discretizations for Semilinear Parabolic Equations
• Nonlinear Schrödinger evolution equations
• On multistep-Galerkin discretizations of semilinear hyperbolic and parabolic equations
• Semidiscrete and single step fully discrete approximations for second order hyperbolic equations
• Blow-up in Nonlinear Schroedinger Equations-I A General Review
• On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
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