# Publications

Here is my google scholar page.

An up-to-date copy of my CV can be found here and below is a list of my publications:

- M. Vynnycky, S.L. Mitchell, "On the numerical solution of a Stefan problem with finite extinction time", Journal of Computational and Applied Mathematics, 276, 98-109, 2015.
- S.L. Mitchell, M. Vynnycky, "The oxygen diffusion problem: analysis and numerical solution", Applied Mathematical Modelling, 39, 2763-2776, 2015.
- S.L. Mitchell, "Applying the combined integral method to two-phase Stefan problems with delayed onset of phase change", Journal of Computational and Applied Mathematics, 281, 58-73, 2015.
- F. Font, T.G. Myers, S.L. Mitchell, "A mathematical model for nanoparticle melting with density change", Microfluid Nanofluid, 18, 233-243, 2015.
- M. Vynnycky, S.L. Mitchell, B.J. Florio, S.B.G. O'Brien, "Decoupling the interaction of solid and fluid mechanics in the modelling of continuous casting processes", Progress in Industrial Mathematics at ECMI 2014, in press.
- S.L. Mitchell, S.B.G. O'Brien, "The two envelope problem: there is no conundrum", Teaching Mathematics and its Applications, doi:10.1093/teamat/hru019, 2014.
- L.B. Cribbin, H.F. Winstanley, S.L. Mitchell, A.C. Fowler, G.C. Sander, "Reaction front formation in contaminant plumes", Journal of Contaminant Hydrology, 171, 12-21, 2014.
- S.L. Mitchell, "An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue", Applied Mathematical Modelling, 38, 4396-4408, 2014.
- S.L. Mitchell, S.B.G. O'Brien, "Asymptotic and numerical solutions of a free boundary problem for the sorption of a finite amount of solvent into a glassy polymer", SIAM Journal on Applied Mathematics, 74(3), 697-723, 2014.
- S.L. Mitchell, M. Vynnycky, "On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions", Journal of Computational and Applied Mathematics, 264, 49-64, 2014.
- N.A.S. Smith, S.L. Mitchell, A. Ramos, "Analysis and Simplification of a Mathematical Model for High-Pressure Food Processes", Applied Mathematics and Computation, 226, 20-37, 2013.
- M. Vynnycky, S. L. Mitchell, "On the Accuracy of a Finite-Difference Method for Parabolic PDEs with Discontinuous Boundary Conditions", Numerical Heat Transfer, Part B, 64, 275-292, 2013.
- M. Vynnycky, W. T. Lee, S. L. Mitchell, G. Richardson, "Foam formation in the plastics industry", Mathematics-in-Industry Cast Studies Journal, 5, 27-42, 2013.
- F. Font, S. L. Mitchell, T. G. Myers. "One-dimensional solidification of supercooled melts", International Journal of Heat and Mass Transfer, 62, 411-421, 2013.
- T. G. Myers, S. L. Mitchell, "A mathematical analysis of the motion of an in-flight soccer ball", Sports Engineering, 16, 29-41, 2013.
- S. L. Mitchell, S. O. B. O'Brien, "Asymptotic, numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers", Applied Mathematics and Computation, 219, 376-388, 2012.
- S. L. Mitchell, T. G. Myers, "Application of heat balance integral methods to one-dimensional phase change problems", International Journal of Differential Equations, Vol. 2012, 187902, 22 pages.
- T. G. Myers, S. L. Mitchell, F. Font, "Energy conservation in the one-phase supercooled Stefan problem", International Communications in Heat and Mass Transfer, International Communications in Heat and Mass Transfer, 39, 1522-1525, 2012.
- S. L. Mitchell, M. Vynnycky, "An accurate finite-difference method for ablation-type Stefan problems", Journal of Applied and Computational Mathematics, 236, 4181-4192, 2012.
- S. L. Mitchell, "Applying the combined integral method to one-dimensional ablation", Applied Mathematical Modelling, 36, 127-138, 2012.
- S. L. Mitchell, "An accurate nodal heat balance method with spatial subdivision", Numerical Heat Transfer, Part B, 60, 34-56, 2011.
- T. G. Myers, S. L. Mitchell, "Application of the Combined Integral Method to Stefan problems", Applied Mathematical Modelling, 35, 4281-4294, 2011.
- S. L. Mitchell, M. Vynnycky, I. G. Gusev, S. S. Sazhin, "An accurate numerical solution for the transient heating of an evaporating spherical droplet", Applied Mathematics and Computation, 217, 9219-9233, 2011.
- S. L. Mitchell, T. G. Myers, "Improving the accuracy of heat balance methods applied to thermal problems with time dependent boundary conditions", International Journal of Heat and Mass Transfer, 53, 3540-3551, 2010.
- S. L. Mitchell, T. G. Myers, "Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems", SIAM Review, 52(1), 57-86, 2010.
- M. Vynnycky, S. L. Mitchell, "Evaporative cooling and the Mpemba effect", Heat and Mass Transfer, 46, 881-890, 2010.
- T. G. Myers, S. L. Mitchell, "Mathematical Modelling of Phase Change with a Flowing Thin Film", Progress in Industrial Mathematics at ECMI 2010, 399-405.
- S. L. Mitchell, "Approximate solution methods for the one-dimensional Stefan problem with Kinetic Undercooling", 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, July 2010.
- M. Vynnycky, S. L. Mitchell, "On the solution of Stefan problems with delayed onset of phase-change", 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, July 2010.
- S. L. Mitchell, M. Vynnycky, "Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems", Applied Mathematics and Computation, 215, 1609-1621, 2009.
- T. G. Myers, S. L. Mitchell, "Application of the heat balance and refined heat balance integral methods to the Korteweg-de Vries equation", Thermal Science, 13(2), 112-119, 2009.
- T. G. Myers, S. L. Mitchell, G. Muchatibaya, "Unsteady contact melting of a rectangular cross-section phase change material", Physics of Fluids, 20 (103101), 2008.
- S. L. Mitchell, T. G. Myers, "Heat Balance Integral Method for One-Dimensional Finite Ablation", AIAA Journal of Thermophysics and Heat Transfer, 22(3), 508-514, 2008.
- S. L. Mitchell, T. G. Myers, "Approximate solution methods for one-dimensional solidification from an incoming fluid", Applied Mathematics and Computation, 202(1), 311-326, 2008.
- T. G. Myers, S. L. Mitchell, G. Muchatibaya, M. Y. Myers, "A cubic heat balance integral method for one-dimensional melting of a finite thickness layer", International Journal of Heat and Mass Transfer, 50, 5307-5315, 2007.
- S. L. Mitchell, R. Kuske, A. P. Peirce, "An asymptotic framework for the analysis of hydraulic fractures: the impermeable case", Journal of Applied Mechanics, 74, 365-372, 2007.
- S. L. Mitchell, R. Kuske, A. P. Peirce, "An asymptotic framework for finite hydraulic fractures including leak-off", SIAM Journal on Applied Mathematics, 67(2), 364-386, 2007.
- S. L. Mitchell, T. G. Myers, "The laminar-turbulent transition of yield stress fluids in large pipes", Proceedings of the 3rd Mathematics in Industry Study Group, University of Witwatersrand, January 2007.
- S. L. Mitchell, K. W. Morton, A. Spence, "Analysis of box schemes for reactive flow problems", SIAM Journal on Scientific Computing, 27(4), 1202-1225, 2006.