Volume 17, Issue 5
The Numerical Stability of the Theta-Method for Delay Differential Equations with Many Variable Delays
DOI:

J. Comp. Math., 17 (1999), pp. 523-532

Published online: 1999-10

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• Abstract

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs):y'(t) =ay(t) + Sum DD(m, j = 1 .. b_jy(lambda_jt) t >= y_0, where a, b_1, b_2, ... b_m and y_0 \in C, 0 > lambda_m \le \lambda_m-1 \le ... \le \lambda_1). A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear theta-method is OmegaGP_m-stable if and only if SX 1 2 SX \le theta \le 1.

• Keywords

Delay differential equation Variable delays Numerical stability