A conservative exponential time differencing method for the nonlinear cubic Schrödinger equation

DOI10.1080/00207160.2015.1101458zbMath1364.65159OpenAlexW2272382656WikidataQ115552439 ScholiaQ115552439MaRDI QIDQ5737863

A. G. Bratsos, Abdul Q. M. Khaliq

Publication date: 30 May 2017

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2015.1101458

zbMATH Keywords

method of linescubic Schrödinger equationexponential time differencingmodified predictor-corrector

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Numerical efficiency of some exponential methods for an advection–diffusion equation ⋮ An exponential time differencing method of lines for Burgers-Fisher and coupled Burgers equations ⋮ A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting

Cites Work

• Unnamed Item
• Exponential time differencing Crank-Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations
• An engineer's guide to soliton phenomena: Application of the finite element method
• Pseudo-spectral solution of nonlinear Schrödinger equations
• Efficient finite difference solutions to the time-dependent Schrödinger equation
• A finite-difference method for solving the cubic Schrödinger equation
• Exponential time differencing for stiff systems
• A numerical study of the nonlinear Schrödinger equation
• A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
• A study on linear and nonlinear Schrödinger equations by the variational iteration method
• Nonlinear stability of an axial electric field: effect of interfacial charge relaxation
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibres.
• \(B\)-spline finite element studies of the nonlinear Schrödinger equation
• A quadratic B-spline finite element method for solving nonlinear Schrödinger equation
• The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems
• A differential quadrature algorithm for simulations of nonlinear Schrödinger equation
• A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations
• The meshless kernel-based method of lines for the numerical solution of the nonlinear Schrödinger equation
• On Dysthe's nonlinear Schrödinger equation for deep water waves
• AN IMPROVED SECOND-ORDER NUMERICAL METHOD FOR THE GENERALIZED BURGERS–FISHER EQUATION
• A modified numerical scheme for the cubic Schrödinger equation
• On Convergence and Stability of the Explicit Difference Method for Solution of Nonlinear Schrödinger Equations
• Fourth-Order Time-Stepping for Stiff PDEs
• New second- and fourth-order accurate numerical schemes for the nonlinear cubic Schrödinger equation
• A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics

This page was built for publication: A conservative exponential time differencing method for the nonlinear cubic Schrödinger equation