Dr Jason Roberts

Head of Mathematics

Jason graduated from Chester in 1993 with a BSc (Hons) degree in Mathematics & Computer Science. He obtained his MSc in 1996 and his PhD in 2000, both in Mathematics. In 2004 Jason obtained Qualified Teacher Status.

Qualifications

BSc MSc PhD CMath CSci FIMA QTS FHEA

Overview

After graduating with his BSc degree, Jason began working at the University of Chester as a Research Assistant, a role which included tutorial support for students, looking after specialist Mathematics software & hardware and, later on, included visiting lecturer duties. During this time he studied part-time, first for a Masters and then for a PhD, before leading a short NATO-funded research project as part of his post-doctoral research. 

 Whilst being active in academic research, Jason also had a strong interest in teaching and learning and so left the University to obtain a secondary school teaching qualification via employment at a school. After nearly 5 years of secondary school teaching (including some as Head of Department at a small boarding school), Jason returned to the University of Chester, initially in the capacity as a Senior Lecturer and Programme Leader.

Jason is a Chartered Mathematician, Chartered Scientist, Fellow of the Institute of Mathematics and its Applications, the University of Chester’s representative to the London Mathematical Society, a Fellow of the Higher Education Academy and a STEM ambassador.

Teaching

Over the years Jason has taught across a wide variety of modules at all undergraduate levels, with topics including Pure Mathematics for first year students, Calculus, Multivariable Calculus, Probability Theory, Applied Statistics, Linear Programming, Linear Algebra, Computer Programming for Mathematics, Integral Equations, Differential Equations, Numerical Analysis and Mathematical Modelling. In the past, Jason has also delivered modules in Quantitative Methods to students of Business-related degrees.

 At MSc level Jason has also delivered modules focusing on Mathematical Modelling, Differential & Integral Equations and Stochastic Differential Equations.

Jason is keen to use his school teaching experience to help students make the transition from Sixth Form to University and regularly delivers STEM outreach sessions to school pupils to promote Maths and to stay active at the School-University interface.

Research

Jason’s PhD is entitled the Numerical Analysis of Volterra Integro-Differential Equations. His subsequent research continues the theme of numerical analysis of functional differential equations, including forays into applications (including Mathematical Biology & Ecology) of such equations and into stochastic and fractional order equations.

Published work

Articles

  • (with N.J. Ford & C.T.H. Baker), "Preserving qualitative behaviour and transcience in numerical solutions of Volterra integro-differential equations of convolution type: Lyapunov functional approaches", Proceedings of IMACS World Congress, Berlin, July 1997.
  • (with N.J. Ford & J.T. Edwards), "Does Adomian's Decomposition Method provide an effective alternative to conventional numerical techniques for obtaining approximate solutions to a system of nonlinear predator-prey model equations?", Manchester Centre for Computational Mathematics Numerical Analysis Report No. 309, October 1997.
  • (with N.J. Ford & C.T.H. Baker), “Nonlinear Volterra integro-differential equations - Stability and numerical stability of q  methods”, Manchester Centre for Computational Mathematics Numerical Analysis Report No. 311, October 1997.
  • (with N.J. Ford, J.T. Edwards & L. Shaikhet), "Stability of a difference analogue for a nonlinear integro differential equation of convolution type", Manchester Centre for Computational Mathematics Numerical Analysis Report No. 312, October 1997.
  • (with N.J. Ford & C.T.H. Baker), “Nonlinear Volterra Integro-Differential Equations - Stability and Numerical Stability of q  Methods”, The Journal of Integral Equations and Applications, Vol. 10(4), Winter 1998.
  • (with J.T. Edwards), “On the Existence of Bounded Solutions to a Difference Analogue for a Nonlinear Integrodifferential Equation”, International Journal of Applied Science & Computations, Vol. 6(1), 1999.
  • (with J.T. Edwards & N.J. Ford), “A comparison of approximate methods for a system of non-linear predator-prey model equations”, International Journal of Applied Science & Computations, Vol. 6(2), 1999.
  • (with N.J. Ford, J.T. Edwards & L.E. Shaikhet), “Stability of a discrete non-linear integro-differential equation of convolution type”, Stability and Control: Theory and Applications, Vol. 3(1), 2000.
  • (with J.T. Edwards & N.J. Ford), “Numerical approaches to bifurcations in solutions to integro-differential equations”, Proceedings of the fifth Hellenic-European Conference on Computer Mathematics and its Applications (E A Lipitakis, Ed), Vol 1, 2002.
  • (with J.T. Edwards & N.J. Ford), “The numerical simulation of the qualitative behaviour of Volterra integro-differential equations”, Proceedings of Algorithms for Approximation IV, University of Huddersfield, 2002.
  • (with N.J. Ford & J.T. Edwards), “Bifurcations in numerical methods for Volterra integro-differential equations”, International Journal of Bifurcation and Chaos, Vol 13(11), 2003.
  • (with L. Skyner & T. Smith), “Methods of measuring spatial proximity in primates – a comparison”, Primate Eye 83, June 2004.
  • (with L.E. Shaikhet), “Stochastic Volterra integro-differential equations: stability and numerical methods”, Manchester Centre for Computational Mathematics Numerical Analysis Report No. 450, June 2004.
  • (with L. Skyner & T. Smith), “A novel computer program to calculate spatial proximity in captive primates”, Federation Research Newsletter, Volume 5(3), July 2004.
  • (with L.E. Shaikhet), “Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations”, Advances in Difference Equations, Volume 2006 (pages 1-22),2006.
  • (with L.E. Shaikhet), “Asymptotic stability analysis of a stochastic Volterra integro-differential equation with fading memory”, Dynamics of Discrete, Continuous & Impulsive Systems Series B: Applications & Algorithms, Vol 18, 2011.
  • (with D. Savostyanov & E.E. Tyrtyshnikov), “Superfast solution of linear convolutional Volterra equations using QTT approximation”, Journal of Computational and Applied Mathematics, Vol 260 (pages 434-448), 2014.
  • (with B. Qayyum & M. Saeed), “Data aggregation in wireless sensor networks with minimum delay and minimum use of energy: a comparative study”, Proceedings of the 2nd BCS International IT Conference, BCS Learning and Development Ltd, 2014.
  • (with N.G. Joharhjee), "Stability analysis of a continuous model of mutualism with delay dynamics", International Mathematical Forum, Vol 11(10), 2016.
  • (with A. Althumairi) “Introducing delay dynamics to Bertalanffy’s spherical tumour growth model”, Applied Numerical Mathematics Vol 114 (pages 154-164), 2017

Conference Presentations

  • (with N.J. Ford, J.T. Edwards & W.J. Smith), Using MATLAB in the teaching of Mathematical Modelling and Linear Algebra, Annual MATLAB Users Group Conference, October 1994.
  • (with J.T. Edwards), "The solution of certain predator-prey model equations", Northern England Universities Numerical Analysis Colloquium, University of Liverpool, November 1995.
  • (with N.J. Ford), "Preserving qualitative behaviour and transience in numerical solutions of Volterra integro-differential equations of convolution type: Lyapunov functional approaches", 17th Biennial Conference on Numerical Analysis, University of Dundee, June 1997.
  •  (with J.T. Edwards), “The Existence of Bounded Solutions to a Difference Analogue for a Nonlinear Integrodifferential Equation”, IMACS 1998 Conference, Universidad de Alicante, Spain, June 1998.
  • (with J.T. Edwards & N.J. Ford), "The numerical simulation of an integrodifferential equation close to bifurcation points", 16th IMACS World Congress, Lausanne, Switzerland, August 2000.
  • (with J.T. Edwards, N.J. Ford & L. E. Shaikhet), “Stability of a numerical approximation to an integro-differential equation of convolution type”, 16th IMACS World Congress, Lausanne, Switzerland, August 2000.
  •  “Assessing the reliability of approximate solutions to equations from the biological sciences and other areas”, SET for Britain – The 2003 Great British Research and R&D Show, Poster Presentation, Westminster Palace, London, March 2003.
  • (with L.E. Shaikhet), “Numerical analysis of stochastic Volterra integro-differential equations”, Leverhulme International Network: Numerical and analytical solution of stochastic delay differential equations, University of Chester, November 2008.
  • (with L.E. Shaikhet), “Asymptotic stability analysis of a stochastic Volterra integro-differential equation with fading memory”, Leverhulme International Network: Numerical and analytical solution of stochastic delay differential equations, University of Chester, September 2010.
  • (with J. Williams & L. Assas), “Parametric sensitivity analysis of a mathematical model of the human bone remodelling process”, Leverhulme International Network: Numerical and analytical solution of stochastic delay differential equations, University of Chester, September 2011.
  • (with N. Joharjee), "Mutualism models: a comparison via stability analysis", Mathematical Models in Ecology and Evolution, University of York 2013.
  • (with A.I. Althumairi), "Modelling spherical tumour growth with delay differential equations", LMS-sponsored Workshop on Mathematical and Computational Modelling of Biological Systems, Thornton Science Park University of Chester 2015.
  • (with A.I. Althumairi), "Introducing delay dynamics to Bertalanffy's spherical tumour growth model", Fifth International Workshop on Analysis and Numerical Approximation of Singular Problems", Lagos Portugal 2015.