Stability of Runge-Kutta methods for delay integro-differential equations

被引:68
作者
Koto, T [1 ]
机构
[1] Univ Electrocommun, Dept Comp Sci, Chofu, Tokyo 1828585, Japan
关键词
Runge-Kutta methods; delay integro-differential equations; delay-independent stability;
D O I
10.1016/S0377-0427(01)00596-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study stability of Runge-Kutta (RK) methods for delay integro-differential equations with a constant delay on the basis of the linear equation du/dt = Lu(t) + Mu(t - tau) + K integral(t-tau)(t) u(theta) dtheta, where L, M, K are constant complex matrices. In particular, we show that the same result as in the case K = 0 (Koto, BIT 34 (1994) 262-267) holds for this test equation, i.e., every A-stable RK method preserves the delay-independent stability of the exact solution whenever a step-size of the form h = tau/M is used, where m is a positive integer. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:483 / 492
页数:10
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