Christopher A H Paul

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In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of(More)
Delay diierential equations are of suucient importance in modelling real-life phenomena to merit the attention of numerical analysts. In this paper, we discuss key features of delay diierential equations (DDEs) and consider the main issues to be addressed when constructing robust numerical codes for their solution. We provide an introduction to the existing(More)
In honour of Bill Gear on the celebration of his sixtieth birthday. Abstract Given a set of data fU(i) u(i ; p ?)g corresponding to the delay diierential equation u 0 (t; p) = f(t; u(t; p); u((t; p); p); p) for t t 0 (p); u(t; p) = (t; p) for t t 0 (p); the basic problem addressed here is that of calculating the vector p ? 2 R n. (We also consider neutral(More)
The standard technique for obtaining the stability regions of numerical methods for ordinary diierential equations (ODEs) and delay diierential equations (DDEs) is the boundary-locus algorithm (BLA). However, in the case of the DDE y 0 (t) = y(t) + y(t ?) for & 2 R, the BLA often fails to map out the stability region correctly. In this paper we give a(More)
In this paper we are concerned with the development of an explicit Runge-Kutta scheme for the numerical solution of delay diierential equations (DDEs) where one or more delay lies in the current Runge-Kutta interval. The scheme presented is also applicable to the numerical solution of Volterra functional equations (VFEs), although the theory is not covered(More)
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