Publications are all listed below by category in chronological order.
Alternatively you can access my publication list via
I have included links to the pdf of the paper where they are freely available and to the doi of each paper. Submitted versions of many recent papers can also be found on the arXiv.
 Numerical Analysis of Dynamical Systems,
A.M. Stuart and A.R. Humphries, 685 + xxii pages,
Cambridge University Press, Hardback 1996,
Paperback 1998.
 Spurious Solutions of Numerical Methods for Initial Value
Problems, A.R. Humphries. IMA Journal of Numerical Analysis, 13 (1993), 263290.
 RungeKutta Methods for Dissipative and Gradient
Dynamical Systems, A.R. Humphries and A.M. Stuart. SIAM Journal on Numerical Analysis, 31 (1994), 14521485.
 Model Problems in Numerical Stability Theory for Initial
Value Problems, A.M. Stuart and A.R. Humphries. SIAM Review, 36 (1994), 226257.
 The Essential Stability of Local Error Control for
Dynamical Systems, A.M. Stuart and A.R. Humphries.
SIAM Journal on Numerical Analysis, 32 (1995) 19401971.
 Adaptive Methods for semilinear elliptic equations with
critical exponents and interior singularities, C.J. Budd and A.R. Humphries.
Applied Numerical Mathematics 26 (1997) 227240.
 Weak Finite Dimensional Approximations of SemiLinear
Elliptic PDEs With Near Critical Exponents, C.J. Budd and A.R. Humphries.
Asymptotic Analysis 17 (1998) 185220.
 The finite element approximation of Semilinear Elliptic
PDEs with Critical Sobolev Exponents in the cube, C.J. Budd, A.R. Humphries and A.J.
Wathen. SIAM Journal on Scientific Computing 20, (1999) 18751904.
pdf
 Phase Space Error Control for Dynamical Systems, D.J.
Higham, A.R. Humphries and R.J. Wain, SIAM Journal on Scientific Computing 21, (2000) 22752294.
pdf
 Mosaic
solutions and Entropy for Spatially Discrete CahnHilliard
Equations, K.A. Abell, A.R. Humphries and E.S. Van Vleck,
IMA Journal of Applied Mathematics 65 (2000) 219255.
 Mosaic
solutions and Entropy for Spatially Discrete Coupled Phase Transition
Equations, K.A. Abell, A.R. Humphries and E.S. Van Vleck,
Physica D, 155 (2001), 274310.
 Numerical
and analytical estimates of existence regions
for Semilinear Elliptic equations with Critical Sobolev
Exponents in cuboid and cylindrical domains, C.J. Budd and A.R. Humphries.
Journal of Computational and Applied Mathematics 151 (2003), 5984.
open archive pdf
 Phase Space Stability Error Control with Variable Timestepping RungeKutta Methods for Dynamical Systems, A.R. Humphries and R. Vigneswaran,
Applied Numerical Analysis & Computational Mathematics 1 (2004) 469488.
 Computation of Mixed Type Functional Differential Boundary Value Problems,
K.A. Abell, C.E. Elmer, A.R. Humphries and E.S. Van Vleck. SIAM Journal on Applied Dynamical Systems, 4 (2005) 755781.
pdf
 Electromagnetic
twobody problem: recurrent dynamics in the presence of statedependent delay, J. De Luca, N. Guglielmi, A.R. Humphries and A. Politi.
Journal of Physics A, 43 (2010) 205103 (22 pages).
 Front Solutions for Bistable
DifferentialDifference Equations with
Inhomogeneous Diffusion, A.R. Humphries, B.E. Moore, and E.S. van Vleck.
SIAM Journal on Applied Mathematics, 71 (2011) 13741400.
pdf
 Dynamics of a Delay Differential Equation With Multiple State Dependent Delays,
A.R. Humphries, O.A. DeMasi, F.M.G. Magpantay and F. Upham.
Discrete & Continuous Dynamical Systems  A, 32 (2012) 2701  2727.
 Finite Element Boundary Value Integration of
WheelerFeynman Electrodynamics, J. De Luca, A.R. Humphries, and S.B. Rodrigues,
Journal of Computational and Applied Mathematics, 236 (2012), 33193337.
open archive pdf
 BoundaryValue Problem Formulations for Computing Invariant Manifolds and Connecting Orbits in the Circular Restricted Three Body Problem,
R.C. Calleja, E.J. Doedel, A.R. Humphries, A. Lemus, B.E. Oldeman,
Celestial Mechanics and Dynamical Astronomy, 114 (2012) 77  106.
SharedIt pdf
 Synchronization in ecological systems by weak dispersal coupling with time delay,
E. Wall, F. Guichard and A.R. Humphries, Theoretical Ecology, 6 (2013), 405418.
SharedIt pdf

Neutrophil dynamics during concurrent chemotherapy and GCSF administration: Mathematical
modelling guides dose optimisation to minimise neutropenia,
M. Craig, A.R. Humphries, J. Bélair, J. Li, M.C. Mackey, and F. Nekka.
Journal of Theoretical Biology, 385 (2015) 7789 .

Periodic Solutions of a Singularly Perturbed Delay Differential Equation With Two StateDependent Delays,
A.R. Humphries, D.A. Bernucci, R. Calleja, N. Homayounfar and M. Snarski.
Journal of Dynamics and Differential Equations, 28 (2016) 12151263.
SharedIt pdf

A mathematical model of granulopoiesis
incorporating the negative feedback dynamics
and kinetics of GCSF/neutrophil binding and
internalisation,
M. Craig, A.R. Humphries and M.C. Mackey.
Bulletin of Mathematical Biology, 78 (2016) 23042357.
SharedIt pdf

An upper bound
for the halfremoval time of neutrophils from circulation,
M. Craig, A.R. Humphries and M.C. Mackey.
Blood, 128 (2016), 19891991.
pdf
 Normal and pathological dynamics of platelets in humans,
G. Provencher Langlois, M. Craig, A.R. Humphries, M.C. Mackey, J.M. Mahaffy, J. Bélair, T. Moulin, S.R. Sinclair and L. Wang.
Journal of Mathematical Biology, 75 (2017), 14111462.
SharedIt pdf
 Resonance phenomena in a scalar delay differential equation with two statedependent delays, R.C. Calleja, A.R. Humphries and B. Krauskopf.
SIAM Journal on Applied Dynamical Systems, 16 (2017), 14741513.
pdf

Transit and lifespan in neutrophil production: implications for drug intervention,
D. Camara de Souza, M. Craig, T. Cassidy, J. Li, F. Nekka, J. Bélair and A.R. Humphries.
Journal of Pharmacokinetics and Pharmacodynamics, 45 (2018), 5977.
SharedIt pdf

Dynamics of a Mathematical Hematopoietic StemCell Population Model,
D. Camara de Souza and A.R. Humphries.
SIAM Journal on Applied Dynamical Systems, 18 (2019), 808852.
pdf

Generalised LyapunovRazumikhin techniques for scalar statedependent delay differential equations,
F.M.G. Magpantay and A.R. Humphries.
Discrete & Continuous Dynamical Systems  S, 13 (2020) 85104.
Free pdf available

A mathematical model of viral oncology as an instigator of immunooncology,
T. Cassidy and A.R. Humphries.
bioRχiv: 10.1101/429233 [Systems Biology], 2018.
To appear in Mathematical Medicine and Biology.

Equivalences Between Age Structured Models and State Dependent Distributed Delay Differential Equations,
T. Cassidy, M. Craig and A.R. Humphries.
Published on the arxiv as "A Recipe for
State Dependent Distributed Delay Differential Equations", 2018.
arXiv:1811.05930 [qbio.PE]
To appear in Mathematical Biosciences and Engineering.
 Approximation of Dissipative Partial Differential
Equations over Long Time Intervals, 180207 in
Numerical Analysis, 1993,
Proceedings of the 15th Dundee Numerical
Analysis Conference, JuneJuly 1993", (eds. DF
Griffiths and GA Watson), Longman, 1994, AR Humphries, DA Jones
and A.M. Stuart.
 Finite Element Method Solutions for Semilinear Elliptic
PDEs with Critical Sobolev Exponents on Nonspherical 3D
Domains, A.R. Humphries, C.J. Budd and Wathen, 418425 in LT MagalhÃ£es, C Rocha and L
Sanchez, editors,
Equadiff
95 Proceedings of the International Conference on Differential Equations, World
Scientific, 1998.
 Deterministic and Random Dynamical Systems: Theory and Numerics, A.R. Humphries and
A.M. Stuart.
In Modern Methods in Scientific Computing and Applications,
NATO Science Series II, volume 75, Kluwer Academic Publishers, 2002.
 Efficient accurate noniterative breaking point
detection and computation for statedependent delay differential equations., A. Eremin and A.R. Humphries.
12^{th} International Conference on Numerical Analysis and
Applied Mathematics: ICNAAM 2014. AIP Conference Proceedings 1648, (2015) 150006.

A.R. Humphries and F.M.G. Magpantay.
LyapunovRazumikhin techniques for statedependent delay differential equations, 2017.
arXiv:1507.00141v3 [math.DS]
 A.R. Humphries and N. Christodoulou. Phase Space Error Control for
Dynamical Systems, II. University of Sussex, Centre for
Mathematical Analysis and its Applications Research Report no CMAIA0013, 2000.
 A.R. Humphries and R.P. Wilds. Traveling wave solutions of lattice differential equations through an
embedding approach, 2006.