Numerical studies of the cubic non-linear Schrödinger equation

DOI10.1007/s11071-011-0014-6zbMath1246.65186OpenAlexW2045327526MaRDI QIDQ437144

Faisal E. I. Abd Alaal, Mohamed A. Ramadan, Talaat S. El Danaf

Publication date: 17 July 2012

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-011-0014-6

zbMATH Keywords

numerical exampleserror boundsnon-linear Schrödinger equationvon Neumann stabilitynon-polynomial spline

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (8)

Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations ⋮ Numerical solution of the regularized long wave equation using nonpolynomial splines ⋮ Smooth quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions ⋮ Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation ⋮ Numerical investigation of the solutions of Schrödinger equation with exponential cubic B-spline finite element method ⋮ An exponential spline solution of nonlinear Schrödinger equations with constant and variable coefficients ⋮ A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method ⋮ Spatial frequency range analysis for the nonlinear Schrödinger equation

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