A row-type method for stiff differential equations
type: Item
instance of: scholarly article
title: A row-type method for stiff differential equations
zbMATH Open document ID: 0834.65063
DOI: 10.1007/BF02575719
author: A. M. Urbani
published in: Calcolo
publication date: 1995-12-11T00:00:00Z
review text: A modified Rosenbrock method of order three is proposed for the numerical solution of stiff differential systems. The methods under consideration include in the usual Rosenbrock scheme a semiexplicit additional term which requires the solution of a linear system with the same matrix of coefficients used in stages of the current step. This term introduces new free parameters into the formula which can be chosen to improve the accuracy and/or stability of the method. It is shown that with three steps, it is possible to construct a family of \(A\)-stable formulas of order three. Then the available parameters are chosen so that the local truncation error is minimized and an optimal formula is given. Finally, some statistics comparing the new formula with a third-order formula of \textit{P. Kaps} and \textit{P. Rentrop} [Numer. Math. 33, 55-68 (1979; Zbl 0436.65047)] are presented.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 817316
zbMATH Keywords: error bounds
zbMATH Keywords: Rosenbrock method
zbMATH Keywords: stiff differential systems
zbMATH Keywords: stability
reviewed by: Manuel Calvo
MaRDI profile type: Publication
cites work: Q4725642
cites work: A-Stable Methods and Padé Approximations to the Exponential
cites work: Comparing numerical methods for stiff systems of O.D.E:s
cites work: Rosenbrock methods for stiff ODEs: A comparison of Richardson extrapolation and embedding technique
cites work: Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
cites work: A study of Rosenbrock-type methods of high order
cites work: Order conditions for Rosenbrock type methods
cites work: Modified ROW methods for stiff problems
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description: scientific article; zbMATH DE number 817316