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

Wen Suo Zhao, Chang Yin Wang & Guo Feng Zhang

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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 righthand function f(y) satisfy one-side Lipschitz condition < f(y)-f(z),y-z >= v' ||y-z||_2,f:Omega C m to C~m, or another related one-side Lipschitz condition [F(Y)-F(Z),Y-Z]_D <= v" ||Y-Z||~2_D,F:Omega~S C~(ms) to 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 = {}, 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 righthand function f(y) satisfy one-side Lipschitz condition < f(y)-f(z),y-z >= v' ||y-z||_2,f:Omega C m to C~m, or another related one-side Lipschitz condition [F(Y)-F(Z),Y-Z]_D <= v" ||Y-Z||~2_D,F:Omega~S C~(ms) to 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 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 righthand function f(y) satisfy one-side Lipschitz condition < f(y)-f(z),y-z >= v' ||y-z||_2,f:Omega C m to C~m, or another related one-side Lipschitz condition [F(Y)-F(Z),Y-Z]_D <= v" ||Y-Z||~2_D,F:Omega~S C~(ms) to 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.
Wen Suo Zhao, Chang Yin Wang & Guo Feng Zhang. (1970). 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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