Split-step orthogonal spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions

DOI10.1016/j.amc.2011.07.002zbMath1231.65183OpenAlexW2079050082MaRDI QIDQ654662

Shan-shan Wang, Lu-Ming Zhang

Publication date: 29 December 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.07.002

zbMATH Keywords

convergencenumerical experimentsnonlinear Schrödinger equationsolitonsfinite difference methodstime-dependent potentialBose-Einstein condensatesquadrature formulaespectral methodsconservativesplit steporthogonal spline collocation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Uses Software

• COLROW
• ARCELO

Cites Work

• Unnamed Item
• Local spectral time splitting method for first- and second-order partial differential equations
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Orthogonal spline collocation methods for Schrödinger-type equations in one space variable
• The solution of nonlinear Schrödinger equations using orthogonal spline collocation
• Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles
• A split-step Fourier method for the complex modified Korteweg-de Vries equation.
• Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• On Spline Basis Selection for Solving Differential Equations
• FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
• Alternate Row and Column Elimination for Solving Certain Linear Systems
• Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
• On the Construction and Comparison of Difference Schemes
• A Finite Element Collocation Method for Quasilinear Parabolic Equations