✦ LIBER ✦

On error growth functions of Runge-Kutta methods

✍ Scribed by E. Hairer; M. Zennaro

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 617 KB
Volume: 22
Category: Article
ISSN: 0168-9274
DOI: 10.1016/s0168-9274(96)00032-3

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✦ Synopsis

This paper studies estimates of the form Ilyl -~l II ~ ~(hy)llu0-F011, where yl, Yl are the numerical solutions of a Runge-Kutta method applied to a stiff differential equation satisfying a one-sided Lipschitz condition (with constant u). An explicit formula for the optimal function ~(x) is given, and it is shown to be superexponential, i.e., ~(x~)qo(x2) ~< q~(xj + x2) if Xl and x2 have the same sign. As a consequence, results on asymptotic stability are obtained. Furthermore, upper bounds for ~(x) are presented that can be easily computed from the coefficients of the method.

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