An analysis of convergence for two-stage waveform relaxation methods

DOI10.1016/J.CAM.2003.12.031zbMath1059.65067OpenAlexW2030818052MaRDI QIDQ1877184

Roberto Garrappa

Publication date: 16 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.cam.2003.12.031

zbMATH Keywords

convergencenumerical resultscomparison theoremsTheta methodinner/outer waveform relaxation scheme

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (9)

Convergence of waveform relaxation methods for Hermitian positive definite linear systems ⋮ Using waveform relaxation methods to approximate neutral stochastic functional differential equation systems ⋮ Waveform relaxation method for stochastic differential equations with constant delay ⋮ Discrete time waveform relaxation method for stochastic delay differential equations ⋮ Two stage waveform relaxation method for the initial value problems of differential-algebraic equations ⋮ Semi-convergence of parameterized Uzawa waveform relaxation method for a class of differential-algebraic equations ⋮ Two-stage iterations based on composite splittings for rectangular linear systems ⋮ An analysis of convergence for nonstationary two-stage multisplitting waveform relaxation methods ⋮ Two-stage waveform relaxation method for the initial value problems with non-constant coefficients

Cites Work

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• The use of Runge-Kutta formulae in waveform relaxation methods
• On the convergence of the discretized multi-splitting waveform relaxation algorithm
• Comparison theorems for weak splittings of bounded operators
• Remarks on Picard-Lindelöf iteration. II
• Remarks on Picard-Lindelöf iteration
• Convergence analysis of time-point relaxation iterates for linear systems of differential equations
• Remarks on waveform relaxation method with overlapping splittings
• Theorems on M-splittings of a singular M-Matrix which depend on graph structure
• Convergence of nested classical iterative methods for linear systems
• Convergence of Dynamic Iteration Methods for Initial Value Problems
• Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods
• On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

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