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Volume 17, Issue 5
Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions

Shuang-Suo Zhao, Chang-Yin Wang & Guo-Feng Zhang

J. Comp. Math., 17 (1999), pp. 457-462.

Published online: 1999-10

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  • 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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@Article{JCM-17-457, author = {Zhao , Shuang-SuoWang , Chang-Yin and Zhang , Guo-Feng}, title = {Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {5}, pages = {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 $f$. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9117.html} }
TY - JOUR T1 - Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions AU - Zhao , Shuang-Suo AU - Wang , Chang-Yin AU - Zhang , Guo-Feng JO - Journal of Computational Mathematics VL - 5 SP - 457 EP - 462 PY - 1999 DA - 1999/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9117.html KW - AB -

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 $f$. 

Zhao , Shuang-SuoWang , Chang-Yin and Zhang , Guo-Feng. (1999). Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions. Journal of Computational Mathematics. 17 (5). 457-462. doi:
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