Position: Professor, Head of Department Academic qualifications: MSc, PhD (Louvain) NRF rating: B2 Link to personal page
Fields of interest: Science awareness
Research interests: Partial/ordinary differential equations; dynamical systems; numerical analysis (finite element/difference method, boundary element methods, etc.); function spaces (distributions, Sobolev, etc); integral equations of potential theory
Publications over the past five years:
Journal articles
Anguelov R, Djoko JK, Lubuma JM-S Energy properties preserving schemes for Burgers' equation. Numerical Methods for Partial Differential Equations, 24(1)(2008), 41-59
Lubuma JM-S Fourier series and integral equation method for the exterior Stokes problem. Numerical Methods for Partial Differential Equations, 24(3)(2008), 699-727
Ibijola EA, Lubuma JM-S, Ade-Ibijola OA On nonstandard finite difference schemes for initial value problems in ordinary differential equations. International Journal of Physical Sciences 3(2)(2008), 59-64
Lubuma JM-S, Patidar KC Towards the implementation of the singular function method for singular perturbation problems. Applied Mathematics and Computation, 209(2009), 68-74
Lubuma JM-S, Patidar KC Reliable finite element methods for self-adjoint singular perturbation problems. Quaestiones Mathematicae 32(2009), 397-413 Anguelov, R, Lubuma JM-S, Minani F A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method. Mathematical Methods in the Applied Sciences 33(2010), 41-48
Anguelov R, Lubuma JM-S, Minani F Total variation diminishing nonstandard finite difference schemes for conservation laws. Mathematical and Computer Modelling, 51(2010), 160-166
Chin PM, Djoko JK, Lubuma J-MS Reliable numerical schemes for a linear diffusion equation on a nonsmooth domain. Applied Mathematics Letters 23(2010), 544-548
Garba S, Gumel A, Lubuma JM-S Dynamically-consistent non-standard finite difference method for an epidemic model. Mathematical and Computer Modelling, 53(2011), 131-150
Anguelov R, Lubuma JM-S, Shillor M Topological dynamic consistency of non-standard finite difference schemes for dynamical systems. Journal of Difference Equations and Applications, 17(12)(2011), 1769-1791 Anguelov R, Dumont, Y, Lubuma JM-S Mathematical modeling of sterile insect technology for control of anopheles mosquito. Computers and Mathematics with Applications, 64(2012), 374-389
Chapwanya M, Lubuma JM-S, Mickens RE From enzyme kinetics to epidemiological models with Michaelis-Menton contact rate: Design of nonstandard finite difference schemes. Computers & Mathematics with Applications, 64(2012), 201-213
Chapwanya M, Lubuma JM-S, Mickens RE Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations. Numerical Methods for Partial Differential Equations, 29(1)(2013), 337-360
Anguelov R, Dumont Y, Lubuma JM-S, Mureithi EW Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model. Mathematical Population Studies, 20(2013), 101-122
Anguelov R, Dumont Y, Lubuma JM-S, M Shillor Dynamically consistent nonstandard finite difference schemes for epidemiological models. To appear in Journal of Computational and Applied Mathematics
Books and/or Chapters in books
Lubuma, JM-S. 2009, Symposium onProperties Preserving Numerical Schemes for Differential Equations, In: T Simos, G. Psihoyios and Ch. Tsitouras (Eds), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 18 – 22 September 2009, Rethymno, Crete, Greece, American Institute of Physics-AIP ConferenceProceedings 1168, Vol. 2, pp. 1204-1216.
Conference proceedings
Dumont Y, Lubuma JM-S Comparison of non-standard finite difference methods for vibro-impact systems, In B.R. Andrievsky and AL Fradkov (Eds): CD-Rom Proceedings of Sixth EuroMech Nonlinear Dynamics Conference-ENOC 2008 (30 June – 4 July 2008, Saint Petersburg, Russia), 7 pages. Anguelov R, Djoko JK and Lubuma JM-S Numerical schemes that preserve properties of the solutions of the Burgers equation for small viscosity. In: A Abdulle, J Banasiak, A Damlamian and M Sango (Eds), Multiscale problems in biomathematics, physics and mechanics: modeling, analysis and numerics (Proceedings of the CIMPA School, 6-18 August 2007, Muizenberg, South Africa), Gakuto International Series in Mathematical Sciences and Applications, Vol 3, pp 277-300, ISBN 978-4-7625-0456-3 C3041 Anguelov R, Dumont Y, Lubuma JM-S and Shillor Comparison of some standard and nonstandard numerical methods for the MSEIR epidemiological model, In : T. Simos, G. Psihoyios Ch Tsitouras (eds), Proceedings of International Conference on Numerical Analysis and Applied Mathematics, 18 – 22 September 2009, Rethymno, Crete, Greece, American Institute of Physics-AIP ConferenceProceedings 1168, Vol. 2, pp 1209-1212
Anguelov R, Dumont Y, Lubuma JM-S and Shillor M Dynamically consistent nonstandard finite difference schemes for the MSEIR epidemiological model, In : T Simos, G Psihoyios Ch Tsitouras (eds), Proceedings of International Conference on Numerical Analysis and Applied Mathematics, 18 – 22 September 2009, Rethymno, Crete, Greece, American Institute of Physics-AIP ConferenceProceedings 1168, Vol. 2, pp 1213-1216
Anguelov R, Lubuma JM-S and Shillor M Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. In X Hou, X Lu, A Miranville, J Su and J Zhu (eds), Dynamical Systems and Differential Equations, Proceedings of the 7th AIMS Conference, University of Texas at Arlington, Texas, USA), American Institute of Mathematical Sciences, 2009, pp 34-43, ISBN-10: 1-60133-011-1, ISSN-13: 978-1-60133-011-6
Mureithi EW, Lubuma JM-S A vector-borne epidemic disease model with treatment. In AG Ahmad, AR Salleh, AM Ishak, AS Rambely, H Ismail, LC Yeub, M Darus, NJZ Mamat, NRM Suradi, R Ahmad, RM Nazar, SH Jaaman and Z Isa (eds.), Proceedings of the 2nd International Conference on Mathematical Sciences (ICMS2) 2010, (Kuala Lumpur, Malaysia), University of Kebangsaan, Malaysia, 2010, pp 758-765, ISBN: 978-967-5878-03-9
Lubuma JM-S, Mureithi EW, Terefe Y Analysis and dynamically consistent numerical schemes for the SIS model and related reaction diffusion equation. In CI Christov and MDTodorov (eds), Proceedings of the 3rd International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (Albena, Bulgaria), American Institute of Physics - AIP Conference Proceedings 1404, (2011), pp 168-175, ISBN: 978-0-7354-0976-7
Anguelov R, Dumont Y, Lubuma JM-S, Mathematical modeling of sterile insect technology for control of Anopheles Mosquito. In CI Christov and MDTodorov (eds), Proceedings of the 3rd International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (Albena, Bulgaria), American Institute of Physics - AIP Conference Proceedings 1404, (2011), pp 155-161, ISBN: 978-0-7354-0976-7
Anguelov R, Dumont Y, Lubuma JM-S On non-standard finite difference schemes in Biosciences. In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 212-223, ISBN: 978-0-7354-1099-2
Anguelov R, Lubuma JM-S Mathematical Analysis of vector-borne diseases on plants. In M Kang, Y Dumont and Y Guo (editors), 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA’12), (Shanghai, China), Institute of Electrical and Electronic Engineers (IEEE), Inc, 2012, pp 22-29, ISBN: 978-1-4673-0068-1
Lubuma JM-S, Mickens RE Diffusion versus cross diffusion in Biosciences: challenges in designing nonstandard finite difference schemes. In RJ Daverman, G Benkart, ML Lapidus, M Miller and SH Weintraub (editors), Abstracts of papers presented to the American Mathematical Society (AMS), (San Diego, USA), American Mathematical Society, 2013, 34(1)(171)(2013), pp 265, ISSN: 0192-5857
Last edited by: Ronel Oosthuizen