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:Ω⊆Cm→Cm, or another related one-side Lipschitz condition [F(Y)−F(Z),Y−Z]D≤v″||Y−Z||2D,F:Ωs⊆Cms→Cms, 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