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

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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