Sets of convergence and stability regions

DOI10.1007/BF01937277zbMath0633.65064OpenAlexW2062543345MaRDI QIDQ1096344

Ulla Miekkala, Olavi Nevanlinna

Publication date: 1987

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01937277

zbMATH Keywords

stabilityconvergencelinear systemsparallel computingsplittingmultistep methodsmodularitytime discretizationwaveform relaxationtime iterationsdynamic iterations

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (21)

Implementing an ODE code on distributed memory computers ⋮ A note on the convergence of discretized dynamic iteration ⋮ On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations ⋮ Preconditioning waveform relaxation iterations for differential systems ⋮ A note on windowing for the waveform relaxation method ⋮ Dynamic iteration methods applied to linear DAE systems ⋮ Remarks on Picard-Lindelöf iteration ⋮ Chaotic waveform relaxation methods for dynamical systems ⋮ Pseudospectra of wave from relaxation operators ⋮ A waveform relaxation Newmark method for structural dynamics problems ⋮ Quasinilpotency of the operators in picard-lindelöf iteration ⋮ Remarks on Picard-Lindelöf iteration. II ⋮ Metodi waveform relaxation per la risoluzione numerica di grandi sistemi di equazioni differenziali ordinarie ⋮ Newton waveform relaxation method for solving algebraic nonlinear equations ⋮ Waveform relaxation methods for functional differential systems of neutral type ⋮ Convergence analysis of waveform relaxation methods for neutral differential-functional systems ⋮ Chebyshev acceleration of Picard-Lindelöf iteration ⋮ Parallel methods for initial value problems ⋮ The use of Runge-Kutta formulae in waveform relaxation methods ⋮ Power bounded prolongations and Picard-Lindelöf iteration ⋮ Runge-Kutta methods of dynamic iteration for index-2 differential-algebraic equations

Cites Work

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• p-cyclic matrices and the symmetric successive overrelaxation method
• Stability and accuracy of time discretizations for initial value problems
• Convergence of Dynamic Iteration Methods for Initial Value Problems
• Relaxation-Based Electrical Simulation
• On the equivalence of SOR, SSOR and USSOR as applied to  1-ordered systems of linear equations

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