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- Kate A. Abell, Christopher E. Elmer, A. R. Humphries, Erik S. Van Vleck
- SIAM J. Applied Dynamical Systems
- 2005

We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to theâ€¦ (More)

- Morgan Craig, A. R. Humphries, Michael C. Mackey
- Bulletin of mathematical biology
- 2016

We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freelyâ€¦ (More)

- Andrew M. Stuart, A. R. Humphries
- SIAM Review
- 1994

- Desmond J. Higham, A. R. Humphries, R. J. Wain
- SIAM J. Scientific Computing
- 2000

Variable time-stepping algorithms for initial value ordinary differential equations are traditionally designed to solve a problem for a fixed initial condition and over a finite time. It can be shownâ€¦ (More)

- Renato C. Calleja, Eusebius J. Doedel, A. R. Humphries, A. Lemus-RodrÃguez, E. B. Oldeman

We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differentialâ€¦ (More)

We study the dynamics of a linear scalar delay differential equation ÎµuÌ‡(t) = âˆ’Î³u(t) âˆ’ N âˆ‘ i=1 Îºiu(tâˆ’ ai âˆ’ ciu(t)), which has trivial dynamics with fixed delays (ci = 0). We show that if the delaysâ€¦ (More)

- Morgan Craig, A. R. Humphries, Fahima Nekka, Jacques BÃ©lair, Jun Li, Michael C. Mackey
- Journal of theoretical biology
- 2015

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design,â€¦ (More)

- Daniel CÃ¢mara De Souza, Morgan Craig, +4 authors A. R. Humphries
- Journal of Pharmacokinetics and Pharmacodynamics
- 2017

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartinoâ€™s extensionâ€¦ (More)

- John Budd, A. R. Humphries
- 1996

We make a formal study of the diierential equation u rr + 2 r u r + u + u 5+" = 0; u r (0) = u(1) = 0; u > 0 if 0 6 r < 1 (1) when posed as a variational problem over a nite dimensional subset S h ofâ€¦ (More)

- INTERIORSINGULARITIESC. J. Budd, A. R. Humphries
- 1996

We consider the eeectiveness adaptive nite-element methods for nding the nite element solutions of the parametrised semi-linear elliptic equation u+u+u 5 = 0; u > 0, where u 2 C 2 ((); for a domainâ€¦ (More)