Numerical solution of the Cauchy problem for a system of differential-algebraic equations with the use of implicit Runge-Kutta methods with a nontrivial predictor
type: Item
instance of: scholarly article
title: Numerical solution of the Cauchy problem for a system of differential-algebraic equations with the use of implicit Runge-Kutta methods with a nontrivial predictor
zbMATH Open document ID: 0951.65073
author: G. Yu. Kulikov
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-07-02T00:00:00Z
review text: Three classes of combined numerical methods for solving the Cauchy problem for a system of differential-algebraic equations with a nontrivial predictor are suggested. For these methods, convergence theorems are proved and the estimates of accuracy solution are obtained. Numerical methods with fixed and automatically selected integration steps are considered. Among the mentioned classes of methods, the class requiring the least computational time is found. The obtained results are illustrated by numerical examples.
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 1467855
zbMATH Keywords: system of differential-algebraic equations
zbMATH Keywords: numerical examples
zbMATH Keywords: predictor
zbMATH Keywords: error bounds
zbMATH Keywords: stepsize control
zbMATH Keywords: Cauchy problem
zbMATH Keywords: convergence
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1467855