An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations-Reference-Cited by-同舟云学术

An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations

Published:1979 Issue:146 Volume:33 Page:521-534
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Steihaug Trond,Wolfbrandt Arne

Abstract

A class of linear implicit methods for numerical solution of stiff ODE’s is presented. These require only occasional calculation of the Jacobian matrix while maintaining stability. Especially, an effective second order stable algorithm with automatic stepsize control is designed and tested.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1979-33-146/S0025-5718-1979-0521273-8/S0025-5718-1979-0521273-8.pdf

Reference7 articles.

1. Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations;England, R.;Comput. J.,1969

2. W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of o.d.e.:s," BIT, v. 15, 1975, pp. 1-10.

3. S. P. NØRSETT, Semi-Explicit Runge-Kutta Methods, Technical Report 6, Dept. of Math., Univ. of Trondheim, 1974.

4. Attainable order of rational approximations to the exponential function with only real poles;Nørsett, Syvert P.;Nordisk Tidskr. Informationsbehandling (BIT),1977

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