Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Two classes of internally $ S$-stable generalized Runge-Kutta processes which remain consistent with an inaccurate Jacobian


Authors: J. D. Day and D. N. P. Murthy
Journal: Math. Comp. 39 (1982), 491-509
MSC: Primary 65L20
MathSciNet review: 669642
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Generalized Runge-Kutta Processes for stiff systems of ordinary differential equations usually require an accurate evaluation of a Jacobian at every step. However, it is possible to derive processes which are Internally S-stable when an accurate Jacobian is used but still remain consistent and highly stable if an approximate Jacobian is used. It is shown that these processes require at least as many function evaluations as an explicit Runge-Kutta process of the same order, and second and third order processes are developed. A second class of Generalized Runge-Kutta is introduced which requires that the Jacobian be evaluated accurately less than once every step. A third order process of this class is developed, and all three methods contain an error estimator similar to those of Fehlberg or England.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L20

Retrieve articles in all journals with MSC: 65L20


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0669642-X
PII: S 0025-5718(1982)0669642-X
Keywords: Generalized Runge-Kutta procedure, semi-implicit Runge-Kutta procedure, approximate Jacobian, stiff differential equations, L-stability, A-stability, S-stability, Internal S-stability
Article copyright: © Copyright 1982 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia