The effect of the stopping of the Newton iteration in implicit linear multistep methods

DOI10.1016/0168-9274(95)00064-2zbMath0837.65080OpenAlexW1998397055MaRDI QIDQ1902087

Marc N. Spijker

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)00064-2

zbMATH Keywords

error boundsNewton iterationstiff nonlinear initial value problemsimplicit linear multistep methodsstopping effect

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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)

Related Items

Stiffness in numerical initial-value problems ⋮ CWI contributions to the development of parallel Runge-Kutta methods

Cites Work

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• On the convergence of multistep methods for nonlinear stiff differential equations
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• Remarks on the stability of high-index DAEs with respect to parametric perturbations
• The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Unconditional Convergence of Some Crank-Nicolson Lod Methods for Initial- Boundary Value Problems
• The Order of Convergence of General Linear Methods for Ordinary Differential Equations
• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems
• The automatic integration of ordinary differential equations
• A stopping criterion for the Newton-Raphson method in implicit multistep integration algorithms for nonlinear systems of ordinary differential equations

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