On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation

DOI10.1051/m2an/1991250606431zbMath0744.65085OpenAlexW2464114944MaRDI QIDQ3984727

Vassilios A. Dougalis, Georgios D. Akrivis

Publication date: 27 June 1992

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193643

zbMATH Keywords

error estimatesRunge-Kutta methodslinear Schrödinger equationfully discrete Galerkin methodsconservative, highly accurate Galerkin methodsGauss- Legendre schemes

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Applications to the sciences (65Z05)

Related Items (7)

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation ⋮ Error estimates for finite element methods for a wide-angle parabolic equation ⋮ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equation ⋮ Stability and convergence of Dufort-Frankel-type difference schemes for a nonlinear Schrödinger-type equation ⋮ Numerical methods for a class of generalized nonlinear Schrödinger equations ⋮ Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method

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