Convergence of Runge-Kutta Methods for Delay Differential Equations

被引：0
作者：
K. J. In 't Hout
机构：
[1] University of Leiden,Mathematical Institute
来源：
BIT Numerical Mathematics | 2001年 / 41卷
关键词：
Delay differential equations; initial value problems; numerical solution; Runge-Kutta methods; equistage interpolation; convergence; order conditions;
D O I：
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学科分类号：
摘要：
This paper deals with the adaptation of Runge—Kutta methods to the numerical solution of nonstiff initial value problems for delay differential equations. We consider the interpolation procedure that was proposed in In 't Hout [8], and prove the new and positive result that for any given Runge—Kutta method its adaptation to delay differential equations by means of this interpolation procedure has an order of convergence equal to min {p,q}, where p denotes the order of consistency of the Runge—Kutta method and q is the number of support points of the interpolation procedure.
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页码：322 / 344
页数：22
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