On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations

DOI10.1016/0168-9274(95)00052-VzbMath0836.65087OpenAlexW1980309222MaRDI QIDQ1902073

Karel J. in 't Hout

Publication date: 7 January 1996

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00052-v

zbMATH Keywords

convergenceiterationsystemsparallel computationerror boundsstiff equationsnonlinearsplittingRunge-Kutta methodscomparisonsnon-uniform gridswaveform relaxation methodsalgebraic stability

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

Zero-stability of waveform relaxation methods for ordinary differential equations ⋮ Convergence of waveform relaxation methods for neutral delay differential equations ⋮ 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 ⋮ Newton waveform relaxation method for solving algebraic nonlinear equations ⋮ Convergence analysis of waveform relaxation methods for neutral differential-functional systems ⋮ On the convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems ⋮ A note on discrete dynamic iterations of stiff index-2 DAE's ⋮ Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems ⋮ CWI contributions to the development of parallel Runge-Kutta methods ⋮ An iterated pseudospectral method for delay partial differential equations ⋮ On the convergence of waveform relaxation methods for differential-functional systems of equations

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• A Note on Unconditional Maximum Norm Contractivity of Diagonally Split Runge–Kutta Methods

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