Stability of backward Euler multirate methods and convergence of waveform relaxation

DOI10.1007/BF01994887zbMath0760.65086OpenAlexW1968125459MaRDI QIDQ1196880

Stig Skelboe, Jørgen Sand

Publication date: 16 January 1993

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01994887

zbMATH Keywords

monotonicityconvergencenumerical examplewaveform relaxationmonotonic systemsmonotonical stabilitymultirate backward Euler method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Cites Work

• Unnamed Item
• Unnamed Item
• Multirate linear multistep methods
• On nonlinear difference and differential equations
• On the relation between stability and contractivity
• Remarks on Picard-Lindelöf iteration
• Stability properties of backward differentiation multirate formulas
• M-matrix characterizations. I: nonsingular M-matrices
• Contractivity in the numerical solution of initial value problems
• On Logarithmic Norms
• Contractive methods for stiff differential equations Part II
• Stability Properties of Backward Euler Multirate Formulas