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Contractivity of continuous Runge-Kutta methods for delay differential equations

✍ Scribed by A. Bellen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
849 KB
Volume
24
Category
Article
ISSN
0168-9274

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✦ Synopsis

In this paper the author investigates the stability of numerical methods for general delay differential equations of the type { y'(t) = j(t, y(t), y(a(t))), t 2 to,

where a(t) < t and y(t) is a vector complex-valued function. Contractivity conditions are found for Runge-Kutta methods as applied to linear and nonlinear scalar equations. As for systems, a general condition is found for the contractivity of the solution of (1) in any vector norm, and a numerical method is proposed which preserves the contractivity in the maximum norm. o 1997 Elsevier Science B.V.

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