A procedure with stepsize control for solving \(n\) one-dimensional IVPs

DOI10.1016/j.matcom.2007.11.004zbMath1168.65047OpenAlexW2077630417MaRDI QIDQ955284

Hamed Shariat Yazdi, Davod Khojasteh Salkuyeh, Faezeh Toutounian

Publication date: 19 November 2008

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2007.11.004

zbMATH Keywords

numerical resultsRunge-Kutta methodinitial-value problemroundoff errorsstepsize controlmulti-step methodCADNA librarysingle-step methodCESTAC stochastic arithmetic methodpredictor-corrector routine

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (max. 100)

The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations ⋮ Stepsize control for cubic spline interpolation

Uses Software

• CADNA

Cites Work

• A dynamical strategy for approximation methods
• New methods for evaluating the validity of the results of mathematical computations
• The use of the stochastic arithmetic to estimate the value of interpolation polynomial with optimal degree
• Discrete stochastic arithmetic for validating results of numerical software
• A stochastic scheme for solving definite integrals
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