Melusi Khumalo

Overview

Highest qualification Degree : PhD Institution : Memorial University of Newfoundland Title : Dynamics of Numerics of Linearized Collocation Methods Supervisor : Prof Andrew Foster Field(s) of research Computational Methods Lecturing experience: Applied Mathematics 1 Engineering Mathematics Numerical Methods Linear Algebra Vector Analysis Differential Equations A & B (Honours) List of 20 most recent publications: Chidume. C.E., Khumalo, M. & Zegeye H. Generalized Projection and Approximation of Fixed Points of Non-Self Maps. J ou r na l o f A pp r o xim a ti o n T h e o r y 1 2 0 (2003), 242-252 . Foster, A.E.D, Khumalo, M. Transformation of local bifurcations under collocation methods . J. K o r e a n M a t h.So c . 4 8 (2011), 1101 – 1123. Dlamini, P.G. & Khumalo, M. On the Computation of Blow-up Solutions for Semilinear ODEs and Parabolic PDEs. M a t h em a tic a l P r ob le m s in Eng i n ee r i ng , vol. 2012, Article ID 162034, 15 pages, 2012. doi:10.1155/2012/162034 Dlamini, P.G. & Khumalo, M. On the computation of blow-up solutions for nonlinear Volterra integro- differential equations. M a t h e m a tic a l P r ob lems in Eng i n ee r i ng , vol. 2012, vol. 2012, Article ID 878497, 11 pages, 2012. doi:10.1155/2012/878497. 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. 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. 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 . 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 . 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 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 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. 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 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 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 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. 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. Awad FG, Ahamed SMS, Sibanda P, Khumalo M (2015) The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface. PLoS ONE10(8): e0135914.doi:10.1371/journal.pone.0135914 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 Wang, H. , Yang, Z. and Khumalo, M. (2017) Cordial Volterra Integral Equations with Vanishing Delays. Journal of Applied Mathematics and Physics, 5, 294-302. doi: 10.4236/jamp.2017.52026. Supervision information: Masters: Numerical Simulation of finite time blow up in nonlinear ODEs, Reaction-diffusion equations and Volterra Integro-differential equations (Dlamini, PG: 2012) The new spectral ADM and its higher order based iterative schemes for solving highly nonlinear two-point boundary value problems (Mdziniso, MM: 2014) Numerical solutions for a class of nonlinear Volterra integral equation (Malindzisa, HS: 2015) Spectral relaxation and bivariate local linearization method for solving nonlinear fluid flow problems (Mkhatshwa, MP: 2016) PhD: Applications of linearized perturbations of the Schwarzschild geometry within the Bondi-Sachs formalism (Kubeka, A [UNISA], co-supervisor: 2013) On spectral Relaxation and compact finite difference schemes for ordinary and partial differential equations (Dlamini, PG: 2015)