On convergence of difference schemes for nonlinear Schrödinger equations, the Kuramoto-Tsuzuki equation, and reaction-diffusion type systems

DOI10.1007/BF02335388zbMath0834.65086OpenAlexW2027865520MaRDI QIDQ1897896

Feliksas Ivanauskas

Publication date: 18 September 1995

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02335388

zbMATH Keywords

stabilityconvergencedifference schemesnonlinear Schrödinger equationsKuramoto-Tsuzuki equationimplicit Crank-Nicolson schemereaction-diffusion type systems

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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 (10)

The convergence and stability of splitting finite-difference schemes for nonlinear evolutionary equations ⋮ On a general method for investigation of finite difference schemes ⋮ On convergence and stability of difference schemes for derivative nonlinear evolution equations ⋮ On convergence and stability of difference schemes for nonlinear Schrödinger type equations ⋮ A numerical algorithm for simulation of the Q-switched fiber laser using the travelling wave model ⋮ Linearly Compact Difference Scheme for the Two-Dimensional Kuramoto-Tsuzuki Equation with the Neumann Boundary Condition ⋮ A fourth-order split-step pseudospectral scheme for the Kuramoto-Tsuzuki equation ⋮ Optimal \(L^{\infty}\) error estimates for finite element Galerkin methods for nonlinear evolution equations ⋮ Stability and convergence of difference scheme for nonlinear evolutionary type equations ⋮ A robust semi-explicit difference scheme for the Kuramoto-Tsuzuki equation

Cites Work

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• Difference schemes for nonlinear equations of Schrödinger and parabolic type
• Convergence of the pseudospectral method for the Ginzburg-Landau equation
• Multiplicative estimate of the norm of a function in \(\mathbb{C}\) in terms of the norms \(L_2,W_2^n\) and convergence of the difference methods for nonlinear evolution equations
• Convergence and stability of the difference schemes for a system of nonlinear Schrödinger type equations
• Convergent Extensions of Grid-Functions

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