Name: Abba Gumel
Birthplace: Jigawa State, Nigeria.
Mathematics, Brunel University, England. 1993.
area: parallel and sequential algorithms for parabolic partial
Professor, Department of Mathematics, University of Manitoba,
Research Interests: Scientific Computing, Mathematical
Biology, Dynamical Systems, Modelling, Numerical Analysis.
Gumel: Born in Nigeria, received his Ph.D. in Computational
Mathematics from Brunel University in England and is now a tenured
Associate Professror at the University of Manitoba in Canada.
He has been making significant contributions
in many areas of Applied Mathematics including:
(1) Mathematical Biology: designing and qualitatively analysing
mathematical models for emerging and re-emerging infectious diseases,
aimed at assessing and determining optimal control strategies
for an epidemic.
(2) Non-linear Dynamical Systems: Designining and using Dynamical
Systems theories and tools to investigate the asymptotic dynamical
behaviour of some real-life systems which are formulated in the
form of deterministic, non-linear, ordinary differential equation
(3) Computational Mathematics: Gumel's earlier work on Computational
Mathematics was based on the design of efficient L_0-stable methods,
via the use of the method of lines semi-discretization approach,
for solving multi-dimensional partial differential equations.
Gumel's main contribution in this area includes the design of
a new family of L_0-stable methods which enable the solution of
second-order linear parabolic and hyperbolic partial differential
equations with or without time-dependent source terms to be computed
on a parallel architecture, with each processor solving a linear
algebraic system at every time step using real arithmetic (as
against the computationally-expensive complex arithmetic which
is often required in the process).
In collaboration with Ronald
Mickens, Gumel has, over the last few years, being actively
involved in the construction and theoretical framework of a new
class of finite-difference methods (non-standard methods) invented
by Mickens a few decades ago. This class of methods is highly
robust in capturing the asymptotic dynamics of many classes of
real-life problems. Gumel has edited a special volume of the Journal
of Difference Equations and Applications marking Mickens' 60th
In November of 2003, Dr. Gumel was awarded a Young
African in Mathematics medal by the AMU and the ICMS.
We should note that Professor Gumel's lecture at CAARMS9
was first rate.
Abba Gumel with co-author Ron
Mickens at CAARMS9
- A.B. Gumel, S. Ruan, T. Day, J. Watmough, F. Brauer,
P. Driesche, D. Gabrielson, C. Bowman, M.E. Alexander, S. Ardal,
J. Wu and B.M. Sahai. Modelling strategies for controlling
SARS outbreaks. Proceedings of the Royal Society, Series
B. 271(2004): 2223-2232.
- M.E. Alexander, C. Bowman, A.B. Gumel, S.M. Moghadas,
B.M. Sahai and R. Summers. A vaccination model for transmission
dynamics of influenza. SIAM Journal on Applied Dynamical
Systems. 3(4)(2004): 503-524.
- A.B. Gumel, S.M. Moghadas and R.E.
Mickens. Effect of a preventive vaccine on the dynamics
of HIV transmission. Communications in Non-linear Science
and Numerical Simulations. 9(6)(2004): 649-659.
- A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu. Bifurcation
and stability analyses of a 13-D SEIC model using normal form
reduction and numerical simulations. Dynamics of Continuous,
Discrete and Impulsive Systems, Series B. 10(2003):
- C. Zhen, A.B. Gumel and R.E. Mickens. Nonstandard
discretizations of the generalized Nagumo reaction-diffusion
equation. Numerical Methods for Partial Differential Equations.
- S.M. Moghadas and A.B. Gumel. Dynamical and numerical
analyses of a generalized food-chain model. Applied Mathematics
and Computation. 142(1)(2003): 35-49.
- S.M. Moghadas and A.B. Gumel. A mathematical study
of a model for childhood diseases with non-permanent immunity.
Journal of Computational and Applied Mathematics. 157(2)(2003):
- A.B. Gumel, R.E.
Mickens and B.D. Corbett. A non-standard finite-difference
scheme for a model of HIV transmission and control. Journal
of Computational Methods in Sciences and Engineering.
- A.B. Gumel and S.M. Moghadas. A qualitative study
of a vaccination model with non-linear incidence. Applied
Mathematics and Computation. 143(2-3)(2003): 409-419.
- R.E. Mickens and
A.B. Gumel. Construction and analysis of a nonstandard
finite difference scheme for the Burgers-Fisher equation. Journal
of Sound and Vibration 257 (4)(2002): 791-797.
- A.B. Gumel. A competitive numerical method for a chemotherapy
model of two HIV subtypes. Applied Mathematics and Computation.
- A.B. Gumel. Removal of contrived chaos in finite-difference
methods. International Journal of Computer Mathematics.
- R.E. Mickens and
A.B. Gumel. Numerical study of a nonstandard finite-difference
scheme for the van der Pol equation. Journal of Sound and
Vibration. 250(5)(2002): 955-963.
- A.B. Gumel, Xuewu Zhang, P.N. Shivakumar, M.L. Garba
and B.M. Sahai. A new mathematical model for assessing therapeutic
strategies of HIV infection. Journal of Theoretical Medicine.
- S.M. Moghadas and A.B. Gumel. Global stability of
a two-stage epidemic model with generalized non-linear incidence.
Mathematics and Computers in Simulation. 60(1-2)(2002):
- A.B. Gumel. Numerical modelling of the transmission
dynamics of drug-sensitive and drug-resistant HSV-2.
Communications in Non-linear Science and Numerical
Simulation 6(1)(2001): 23-27.
- P. Yu and A.B. Gumel. Bifurcation and stability analyses
for a coupled Brusselator model. Journal of Sound
and Vibration. 244 (5)(2001): 795-820.
- A.B. Gumel, P.N. Shivakumar and B.M. Sahai.
A mathematical model for the dynamics of HIV-1 during the typical
course of infection. Non-linear Analysis: Theory, Methods
and Applications. 47(3)(2001): 1773-1783.
- W.T. Ang and A.B. Gumel. A boundary integral method
for the three-dimensional heat equation subject to specification
of energy. Journal of Computational and Applied Mathematics.
135 (2)(2001): 303-311.
- A.B. Gumel, T.D. Loewen, P.N. Shivakumar, B.M. Sahai,
P. Yu and M.L. Garba. Numerical modelling of the
perturbation of HIV-1 during combination anti-retroviral therapy.
Computers in Biology and Medicine 31(5)(2001):
- A.B. Gumel, E.H. Twizell and P. Yu. Numerical and
bifurcation analyses of a population model of HIV chemotherapy.
Mathematics and Computers in Simulation. 54, Iss.1-3
- A.B. Gumel, W.F. Langford, E.H. Twizell and J. Wu.
Numerical solutions for a coupled non-linear oscillator.
Journal of Mathematical Chemistry 28(4)(2000):
- A.B. Gumel. On the numerical solution of the diffusion
equation subject to the specification of mass. Journal
of Australian Mathematics Society Series B 40(4)(1999):
- A.B. Gumel Q. Cao and E.H. Twizell. A second-order
scheme for the Brusselator reaction-diffusion system.
Journal of Mathematical Chemistry 26(1999):
- A.B. Gumel and E.H. Twizell. Numerical analysis of
defects caused by thermolysis in an infinite cylindrical ceramic
moulding. Pertanika Journal of Science and Technology.
- A.B. Gumel. Numerical solutions for the canonical
escape equation. South
East Asian Bulletin of Mathematics. 22(1998): 373--380.
- A.B. Gumel, K. Kubota and E.H. Twizell. A sequential
algorithm for the non-linear dual-sorption model of percutaneous
drug absorption. Mathematical
Biosciences. 152(1998): 87--103.
- A.B. Gumel, E.H. Twizell and M.A. Arigu. L_0-stable
parallel methods for multi-dimensional heat equation. Parallel
Algorithms and Applications 11(1997): 13-25.
- A.B. Gumel, E.H. Twizell, M.A. Arigu and F. Fakhr.
Numerical methods for a non-linear system arising in chemical
kinetics. Pertanika Journal of Science and Technology.
- A.B. Gumel, W.T. Ang and E.H. Twizell. Efficient parallel
algorithm for the two-dimensional diffusion equation subject
to the specification of mass. International Journal of
Computer Mathematics. 64 (1+2)(1997): 153-163.
- E.H. Twizell, A.B. Gumel and M.A. Arigu. Second-order,
L_0-stable methods for partial differential equations with
time-dependent boundary conditions. Advances in Computational
Mathematics. 6(3-4)(1996): 333-352.
- M.A. Arigu, E.H. Twizell and A.B. Gumel. Sequential
and parallel methods for solving first-order hyperbolic equations.
Communications in Numerical Methods in Engineering.
- W.T. Ang and A.B. Gumel. Multiple interacting planar
cracks in an inisotropic multi-layered medium under an antiplane
shear stress: A hypersingular integral approach. Engineering
Analysis with Boundary Elements. 2021(1996) 18(Iss.4):
- M.A. Arigu, E.H. Twizell and A.B. Gumel. Parallel
algorithms for second-order hyperbolic equations.
Parallel Algorithms and Applications, 5(1995):
- A.B. Gumel, E.H. Twizell, K. Kubota and M.A. Arigu.
Higher-order parallel methods for a model of percutaneous drug
absorption. International Journal of Computer Mathematics.
- M.A. Arigu, E.H. Twizell and A.B. Gumel. Parallel
algorithms for fourth-order parabolic equations.
Parallel Algorithms and Applications. 5(1995):
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