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 $f$.
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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