A linearized finite-difference method for the solution of some mixed concave and convex non-linear problems

DOI10.1016/J.AMC.2007.07.051zbMath1135.65357OpenAlexW2057513869MaRDI QIDQ2479164

Anouar Ben Mabrouk, Mekki Ayadi

Publication date: 26 March 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.07.051

zbMATH Keywords

stabilityconvergenceconsistencynumerical examplesnonlinear Schrödinger equationfinite-difference scheme

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)

Related Items (4)

Lyapunov type operators for numerical solutions of PDEs ⋮ A note on the numerical solution of the semilinear Schrödinger equation ⋮ Mixed concave-convex sub-superlinear Schrödinger equation: survey and development of some new cases ⋮ Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system

Cites Work

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Multi solitary waves for nonlinear Schrödinger equations
• Nodal solutions for some nonlinear elliptic equations
• Finite difference approximate solutions for a mixed sub-superlinear equation
• Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
• On the blow up phenomenon of the critical nonlinear Schrödinger equation
• On nonlinear schrödinger equations
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