Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions

Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions

Year:    1999

Author:    Shuang-Suo Zhao, Chang-Yin Wang, Guo-Feng Zhang

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 5 : pp. 457–462

Abstract

In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the right-hand function $f(y)$ satisfy one-side Lipschitz condition $$ <f(y)-f(z),y-z> ≤ v' ||y-z||^2,f: \Omega \subseteq C^m → C^m,$$ or another related one-side Lipschitz condition $$[F(Y)-F(Z),Y-Z]_D ≤ v'' ||Y-Z||^2_D, F:\Omega^s \subseteq C^{ms} → C^{ms},$$ this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that $v'-v''$ only is constant independent of stiffness of function $f$. 

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1999-JCM-9117

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 5 : pp. 457–462

Published online:    1999-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords:   

Author Details

Shuang-Suo Zhao

Chang-Yin Wang

Guo-Feng Zhang