Speeding up Newton-type iterations for stiff problems

DOI10.1016/j.cam.2004.12.002zbMath1072.65100OpenAlexW2061656309MaRDI QIDQ557691

R. Rojas-Bello, S. González-Pinto

Publication date: 30 June 2005

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.2004.12.002

zbMATH Keywords

convergencenumerical examplesRunge-Kutta methodsIterative schemesStiff problems

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)

Related Items (4)

An improved approximate Newton method for implicit Runge-Kutta formulas ⋮ Convergence on error correction methods for solving initial value problems ⋮ A modification of Cauchy's method for quadratic equations ⋮ An error embedded method based on generalized Chebyshev polynomials

Uses Software

• NSDTST
• STDTST

Cites Work

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• Triangularly Implicit Iteration Methods for ODE-IVP Solvers
• Iterated Runge–Kutta Methods on Parallel Computers
• Efficiency of Methods for Second-Order Problems
• On the implementation of implicit Runge-Kutta methods
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Two FORTRAN packages for assessing initial value methods
• A Generalization of a Theorem of Bôcher
• The implementation of Runge-Kutta implicit processes
• Implementation of high-order implicit Runge-Kutta methods

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