The convergence and stability of splitting finite-difference schemes for nonlinear evolutionary equations

DOI10.1007/s10986-005-0035-2zbMath1106.65082OpenAlexW2036761403MaRDI QIDQ852291

Mindaugas Radziunas, Feliksas Ivanauskas

Publication date: 28 November 2006

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

Full work available at URL: https://doi.org/10.1007/s10986-005-0035-2

zbMATH Keywords

stabilityconvergenceheat equationSchrödinger equationfinite-difference methodsplitting methodKuramoto-Tsuzuki equationlocally one-dimensional scheme

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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 (1)

ON STABILITY ANALYSIS OF FINITE DIFFERENCE SCHEMES FOR GENERALIZED KURAMOTO-TSUZUKI EQUATION WITH NONLOCAL BOUNDARY CONDITIONS

Cites Work

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• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation
• Numerical methods for evolutionary reaction-diffusion problems with nonlinear reaction terms.
• On convergence of difference schemes for nonlinear Schrödinger equations, the Kuramoto-Tsuzuki equation, and reaction-diffusion type systems
• Numerical study of self-focusing solutions to the Schrödinger-Debye system
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
• IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS
• The method of splitting for solving systems of time-dependent non-linear equations of the Schrödinger type

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