Department of Mathematical Sciences

Prof Melusi Khumalo

College of Science, Engineering and Technology
School of Science
Department: Mathematical Sciences
Acting Chair
Tel: 011 670 9192
Fax: 011 670 9171


  • PhD (Memorial University of Newfoundland, 1998)
  • MSc Numerical Analysis (Brunel University London, 1991)
  • BSc (University of Swaziland, 1988)

Fields of academic interests

  • Computational Fluid Dynamics
  • Numerical Methods for Integral Equations
  • Dynamics of Numerics

Field of Specialisation

  • Numerical Analysis
  • Integral Equations
  • Dynamical Systems

Journal articles

  1. Chidume. C.E., Khumalo, M. & Zegeye H. Generalized Projection and Approximation of Fixed Points of Non-Self Maps. Journal of Approximation Theory 120 (2003), 242-252.

  2. Foster, A.E.D., Khumalo, M. Linearized Collocation Methods, Bifurcations and The Singular Set. Proc. 4th Int. Conf. on Research &  Education in Math: “Meeting Challenges of Global Research and Education in Mathematical Sciences”. Kuala Lumpur, Malaysia, Oct 2009.

  3. Foster, A.E.D, Khumalo, M. Transformation of local bifurcations under collocation methods. J. Korean Math.Soc. 48 (2011), 1101 – 1123.

  4. Dlamini, P.G. & Khumalo, M. On the Computation of Blow-up Solutions for Semilinear ODEs and Parabolic PDEs. Mathematical Problems in Engineering, vol. 2012, Article ID 162034, 15 pages, 2012. doi:10.1155/2012/162034

  5. Dlamini, P.G. & Khumalo, M.    On the computation of blow-up solutions for nonlinear Volterra integro- differential equations.        Mathematical Problems in Engineering, vol. 2012, vol. 2012, Article ID 878497, 11 pages, 2012. doi:10.1155/2012/878497.

  6. Khumalo, M. Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet       Theory.Journal of Applied Mathematics, vol. 2013, Article ID 645345, 11 pages, 2013. doi:10.1155/2013/6453456.

  7. Motsa, S.S., Dlamini, P.G., M. Khumalo. A new multistage spectral relaxation method for solving chaotic  initial value systems, Nonlinear Dynamics, April 2013, Volume 72, Issue 1-2, pp 265-283.

  8. Dlamini, P.G., Khumalo, M., S.S. Motsa. Solving hyper-chaotic systems using the spectral relaxation method.  Abstract and Applied Analysis, vol. 2012, Article ID 203461, 18 pages.   doi:10.1155/2012/203461.

  9. P. G. Dlamini, S. S. Motsa, and M. Khumalo. On the Comparison between Compact Finite Difference and Pseudospectral     Approaches for Solving Similarity Boundary Layer Problems. Mathematical Problems in Engineering, vol. 2013, Article ID 746489, 15 pages, 2013. doi:10.1155/2013/746489.

  10. P. G. Dlamini, S. S. Motsa, and M. Khumalo, “Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer   Flow Problems,” Advances in Mathematical Physics, vol. 2013, Article ID 941096, 10 pages, 2013. doi:10.1155/2013/941096

  11. S. S. Motsa, P. G. Dlamini, and M. Khumalo, “Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems,” Advances in Mathematical Physics, vol. 2014, Article ID 341964, 12 pages, 2014. doi:10.1155/2014/341964

  12. P.G. Dlamini, M. Khumalo and S.S. Motsa, “A note on the multi-stage spectral relaxation method for chaos control and synchronization”, International Journal of Nonlinear Sciences and Numerical Simulation. Volume 15, Issue 5, Pages 289–298, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: 10.1515/ijnsns-2013-0054, July 2014.

  13. H. S. Malindzisa and M. Khumalo, “Numerical Solutions of a Class of Nonlinear Volterra Integral Equations,” Abstract and Applied Analysis, vol. 2014, Article ID 652631, 8 pages, 2014. doi:10.1155/2014/652631

  14. H. S. Malindzisa and M. Khumalo, “Collocation Methods of a Class of Nonlinear Volterra Integral Equations,”  Proceedings of the 14th International Conference on Mathematical Methods in Science and Engineering - Almería , Spain. ISBN: 978-84-616-9216-3

  15. Awad FG, Motsa S, Khumalo M (2014) Heat and Mass Transfer in Unsteady Rotating Fluid Flow with Binary Chemical Reaction and Activation Energy. PLoS ONE 9(9): e107622. doi:10.1371/journal.pone.0107622

  16. S. S. Motsa, F. G. Awad, and M. Khumalo, “Nonlinear Nanofluid Flow over Heated Vertical Surface with Sinusoidal Wall Temperature Variations,” Abstract and Applied Analysis, vol. 2014, Article ID 408230, 11 pages, 2014. doi:10.1155/2014/408230

  17. H.S. Mamba and M. Khumalo, “On the Analysis of Numerical Methods for non-standard Volterra Integral Equation,”  Abstract and Applied Analysis, vol. 2014, Article ID 763160, 7 pages, 2014. doi:10.1155/2014/763160.

  18. Sibanda P, Awad FG, Haroun N, Khumalo M, “On couple stress effects on unsteady nanofluidflow over stretching surfaces with vanishing nanoparticle flux at the wall,” Journal of Applied Fluid Mechanics, Vol. 9, No. 4, pp. 1937-1944, 2016.

  19. Awad FG, Ahamed SMS, Sibanda P, Khumalo M (2015) The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface. PLoS ONE 10(8): e0135914.doi:10.1371/journal.pone.0135914

  20. Mkhatshwa MP, Awad F, Khumalo M. Cross-diffusion effects on unsteady bio-convective flow past a stretching sheet. ASME. J. Heat Transfer. 2016;139(3):031101-031101-11. doi:10.1115/1.4034937

  21. Dlamini, P. & Khumalo, M. (2017). A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations. Open Mathematics, 15(1), pp. 1450-1462.

  22. Mathale, D., Dlamini, P.G. & Khumalo, M. Computational & Applied Mathematics (2018).


  • Collocation Methods for Volterra Integral Equations
  • Analysis and numerical treatment for Cordial Volterra integral equations
  • Multi-domain Spectral Collocation methods