Professor of Computational and Applied Mathematics

Director of Applied Mathematics Research Group. After graduating from Oxford in 1979 with a BA in Mathematics, Neville took his MA (Oxon) in 1983, an MSc (from Manchester in 1986) and a PhD in 1991 from Liverpool.

MA, MSc, PhD

He is leader of the Applied Mathematics Research Group on problems with memory and after effect. He co-ordinates research projects and activities within the Chester group and anybody considering either postgraduate study for a research degree or interested in collaborating with the group are encouraged to make contact with him.

Neville has been involved in the organising and or, as a featured speaker at the following recent conferences:

- International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP) 2004, Lisbson.
- The Second International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP) 2006, Karlovassi, Samos, Greece.
- A4A5 Algorithms for Approximation V, 2005, Chester.
- The 5th & 8th Hellenic European Conferences on Computer Mathematics & its Applications (HERCMA) 2001 and 2007, Athens, Greece.
- Stochastic Evolutionary Problems: Theory, Modelling and Numerics, 2007, Chester.

- Member of the London Mathematical Society
- Member of the Society for Industrial and Applied Mathematics
- Member of the Manchester Centre for Computational Mathematics
- Honorary Research Fellow, University of Manchester
- Member of the EPSRC peer review university
- Reviewer for Zentralblatt Mathematik and Mathematical Reviews.
- Member of the Institute for Teaching and Learning in Higher Education

Interesting fact: Neville is a local preacher in the Methodist church. As well as a utilitarian cyclist (over 5000 miles a year) he keeps rare ducks such as Welsh Harlequins and Call Ducks in his garden.

- Shortcuts
- Teaching
- Research
- Published Work

At Chester he contributes to the teaching of modules in Linear Algebra, Analysis, Delay Differential Equations, Complex Methods, Integral Equations, Functional Differential Equations and Analysis.

Neville specialises in Numerical and Analytical approaches to solving functional differential equations and his teaching reflects his research interests. He has ongoing projects in the following areas: Numerical solution of functional differential equations, (Volterra integral and integro-differential equations, delay differential and integral equations. Fractional differential equations.) Stability theory and qualitative behaviour of solutions.

He is also the programme leader for the BSc Mathematics single and combined honours courses.

Neville enjoys teaching maths for many reasons. He likes questions with precise answers and is particularly interested in trying to make precise statements about approximate answers to problems!

- Numerical approximation of the characteristic values for a delay differential equation, MCCM Technical Report 250, 1999. Download
- Numerical approximation of the characteristic values for a delay differential equation Proceedings of the IMACS World Congress on Mathematics and Computers in Simulation, Lausanne, 2000, 213-7. Download

- Convergence of linear multistep methods for a class of delay integro-differential equations International Series on Numerical Mathematics (1988) 86, 47-59
- Asymptotic error expansions for linear multistep methods for a class of delay integro-differential equations in the Computer Mathematics issue of the Bulletin of the Hellenic Mathematical Society (1991) Reissued as: Asymptotic error expansions for linear multistep methods for a class of delay integro-differential equations in E A Lipitakis (ed) Advances on Computer Mathematics and its applications, World Scientific, Singapore (1993), 59-72
- Some applications of the Boundary-Locus Method and the Method of D-Partitions IMA Journal of Numerical Analysis (1991) 11, 143-158
- Stability properties of a scheme for the approximate solution of a delay integro differential equation Applied Numerical Mathematics (1992) 9, 357-370
- Qualitative behaviour and stability of solutions of discretised non-linear Volterra integral equations of convolution type, MCCM Technical Report no 261, 1994.(ISSN 1360-1725)
- Qualitative behaviour and stability of solutions of discretised non-linear Volterra integral equations of convolution type Journal of Computational and Applied Mathematics 66 (1996) 213-225 (ISSN 0377-0427
- Preserving transience in numerical solution of non-linear Volterra integral equations of Convolution type, MCCM Technical Report no 284, 1995. (ISSN 1360-1725)
- Stability of a Numerical Solution of a Non-linear Volterra Integral Equation of Convolution Type Zeitschritt fur Angewandte Mathematik und Mechanik, 76 S1 (1996) 401-2
- Preserving transient behaviour in numerical solutions of Volterra integral equations of convolution type. Invited paper in the special issue in the series Nonlinear Analysis and Applications (in memorium Professor Günther Hämmerlin) (R Agarwal and D O'Regan (eds)) Integral and integro-differential equations, Gordon and Breach, 1999, 77-89.

- Qualitative behaviour of approximate solutions of some Volterra integral equations with non-Lipschitz nonlinearity MCCM, Report 309, 1997
- Volterra integral equations with non-Lipschitz nonlinearity, Rostocker Mathematisches Kolloquium, (1997) 51, 65-82

Boundedness and stability of difference equations, Journal of Computational and Applied Mathematics 140 (2002) 275-289. Download

- A comparison of Adomian's decomposition method and Runge Kutta methods for approximate solution of some predator prey model equations, MCCM Report 309, 1997 Download
- A comparison of approximate methods for a system of non-linear predator-prey model equations, International Journal of Applied Science and Computations, 6.2, (1999) 80-88
- The numerical solution of an integro-differential equation close to bifurcation points, Proceedings of the IMACS World Congress on Mathematics and Computers in Simulation, Lausanne, 2000, 213-3 Download
- 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), 1, (2002) 109-116. Download
- Bifurcations in numerical methods for Volterra integro-differential equations, International Journal of Bifurcation and Chaos. 13 (2003) 3255-3271
- The numerical simulation of the qualitative behaviour of Volterra integro-differential equations, In J Levesley, I J Anderson & J C Mason (Eds) Algorithms for Approximation IV, University of Huddersfield, 2002, 86-93

- Preserving qualitative behaviour and transience in numerical solutions of non-linear Volterra integro differential equations of convolution type I: Lyapunov functional approaches, Proceedings of the 15th IMACS World Congress, Berlin 1997, 2, 445-450
- Nonlinear Volterra integro-differential equations- Stability and numerical stability of q-methods, MCCM Report 311, 1997. Invited paper to the special issue of the Journal of Integral Equations and Applications honouring Professor P H M Anselone, Vol 10, 4, (1998) 397-416.

- Stability of a difference analogue for a nonlinear integro differential equation of convolution type, MCCM Report 312, 1997
- Stability of a numerical approximation to an integro-differential equation of convolution type, Proceedings of the IMACS World Congress on Mathematics and Computers in Simulation, Lausanne, 2000, 154-3
- Stability of a discrete non-linear integro-differential equation of convolution type, Stability and Control: Theory and Applications, 2000, 3.1, 24-37 (ISSN 1563-3276) Download

- Sensitivity of hospital clinic queues to patient non-attendance, Proceedings of the IMACS Congress on Computer Simulation and Mathematical Modelling, Alicante 1998, 243-248 International Journal of Applied Science and Computations, Vol 7, 3, (2000) 148-154 Download

- The use of boundary locus plots in the identification of Hopf bifurcation points in numerical approximation of delay differential equations, MCCM Report 322, 1998 Presented at the Second International Congress on Numerical Solution of Differential Equations, Coimbra, Portugal, 1998. Journal of Computational and Applied Mathematics 111 (1999) 153-162 (ISSN 0377-0427). Download
- Numerical Hopf bifurcation for the delay logistic equation, MCCM Report 323, 1998
- Hopf bifurcation for numerical approximations to the delay logistic equation, Proceedings of the IMACS Congress on Computer Simulation and Mathematical Modelling, Alicante 1998, 249-254 Download
- Hopf bifurcation for numerical approximations to the delay logistic equation International Journal of Applied Science and Computations, 6.3 (1999) 167-172 Download
- Numerical Hopf bifurcation for a class of delay differential equations. Presented at ICCAM 1998, Journal of Computational and Applied Mathematics 115 (2000) 601-616 (ISSN 0377-0427) Download
- Insight the qualitative behaviour of numerical solutions to some delay differential equations. Presented at HERCMA 1998. Proceedings of the fourth Hellenic European Conference on Computer Mathematics and its applications, (E A Lipitakis Ed) 1999, 2 629-636. Download
- How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation? Journal of Computational and Applied Mathematics, 125, (2001) 277-285 (ISSN 0377-0427). Download

- Numerical modelling by retarded functional differential equations, MCCM Report 335, 1998. Also in E A Lipitakis (Ed) Topics in computer mathematics and its applications, 113-137, LEA Athens. Also in Proceedings of the fourth Hellenic European Conference on Computer Mathematics and its applications, (E A Lipitakis Ed) 1999, 1 16-40. Reissued as: Hellenic European Research on Mathematics and Informatics Science Vol 2, (2001) 29-52.

- Analysis of Fractional Differential Equations, Journal of Mathematical Analysis and Applications, 265 (2002) 229-248. Download
- Numerical solution of the Bagley Torvik equation, BIT 42 (2002) 490-507. Download
- Numerical solution methods for distributed order differential equations, Fractional Calculus and Applied Analysis 4 (2001) 531-542.

- A predictor corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, 29 (2002) 3-22.

- Characterising small solutions in delay differential equations through numerical approximations, Applied Mathematics and Computation 131 (2002) 253-270.Download
- Numerical approximation of delay differential equations with small solutions, an invited minisymposium paper in the Proceedings of the IMACS World Congress on Mathematics and Computers in Simulation, Lausanne, 2000, 173-3.

- The approximate solution of fractional differential equations of order greater than one, Proceedings of the IMACS World Congress on Mathematics and Computers in Simulation, Lausanne, 2000, 213-1. Download
- Numerical and analytical treatment of differential equations of fractional order, Invited paper, in D. Schultz, B. Wade, J. Vigo-Aguiar, S. Dey (eds), proceedings of the IMACS International Conference on Mathematical Modelling and Computers in Simulation, Milwaukee, 2000, p60-65. Download
- The numerical solution of fractional differential equations: speed versus accuracy, Numerical Algorithms, 26 4 2001, 333-346. 4. Download
- Numerical approaches to the solution of some fractional differential equations, Proceedings of the fifth Hellenic-European Conference on Computer Mathematics and its applications (E A Lipitakis, Ed), 1, 2002, 93-100. Download

- The Numerical Solution of Linear Multi-term Fractional Differential Equations: Systems of Equations, Journal of Computational and Applied Mathematics 148, 2002, 401-418. Download

- Parallel implementation of fast wavelet transforms, MCCM Report 389, 2001. Download
- Small-scale Parallel implementation of fast wavelet transforms, in D. Schultz, B. Wade, J. Vigo-Aguiar, S. Dey (eds), proceedings of the IMACS International Conference on Mathematical Modelling and Computers in Simulation, Milwaukee, 2000, p110-115. Download

- Numerical investigation of bifurcations in stochastic delay differential equations, MCCM Technical Report 396, 2002.

with P M Lumb, Chester

- Numerical approaches to delay equations with small solutions, Proceedings of the fifth Hellenic-European Conference on Computer Mathematics and its applications (E A Lipitakis, Ed), 1, 2002, 101-108. Download
- Systems of delay equations with small solutions: a numerical approach, In J Levesley, I J Anderson & J C Mason (Eds) Algorithms for Approximation IV, University of Huddersfield, 2002, 94-101. Download

- Numerical analysis of a singular integral equation, Applied Mathematics and Computation, 167 (2005) 372-382.

- Solution of a singular integral equation by a split-interval method (accepted, to appear in International Journal of Numerical Analysis and Modeling)

- Parallel implementation of fast wavelet transforms, MCCM Report 389, 2001. Download
- Small-scale Parallel implementation of fast wavelet transforms, in D. Schultz, B. Wade, J. Vigo-Aguiar, S. Dey (eds), proceedings of the IMACS International Conference on Mathematical Modelling and Computers in Simulation, Milwaukee, 2000, p110-115. Download

- Numerical investigation of bifurcations in stochastic delay differential equations, MCCM Technical Report 396, 2002.

with P M Lumb, Chester

- Numerical approaches to delay equations with small solutions, Proceedings of the fifth Hellenic-European Conference on Computer Mathematics and its applications (E A Lipitakis, Ed), 1, 2002, 101-108. Download
- Systems of delay equations with small solutions: a numerical approach, In J Levesley, I J Anderson & J C Mason (Eds) Algorithms for Approximation IV, University of Huddersfield, 2002, 94-101. Download

- Numerical analysis of a singular integral equation, Applied Mathematics and Computation, 167 (2005) 372-382.

- Solution of a singular integral equation by a split-interval method (accepted, to appear in International Journal of Numerical Analysis and Modeling)

- Numerical methods for a Volterra integral equation with non-smooth solutions, Journal of Computational and Applied Mathematics, 189 (2006) 412-423
- Numerical methods for a nonuniquely solvable Volterra integral equation, Proceedings of 24th Iberian Latin-American Congress on Computational Methods in Engineering (CD-ROM).

- An algorithm to detect small solutions in delay differential equations, Journal of Computational and Applied Mathematics 193 (2006) 121-139
- Scalar periodic complex delay differential equations: Small solutions and their detection. Accepted, to appear in Proceedings of Algorithms for Approximation V , A.Iske and J.Levesley (eds), Springer-Verlag, Heidelberg (2006) 299-309

- Multi-order fractional differential equations and their numerical solution, Applied Mathematics and Computation 154 (2004) 621-640.

- Detailed error analysis for a fractional Adams method, Numerical Algorithms 36 (2004) 31-52.

- Algorithms for the fractional calculus: a selection of numerical methods, Computational Methods Appl. Mech. Engrg, 194 (2005) 743-773.

- Pitfalls in fast numerical solvers for fractional differential equations, Journal of Computational and Applied Mathematics 186 (2005) 482-503.

- Comparison of Numerical Methods for Fractional Differential Equations Communications in Pure and Applied Analysis, 5 (2006) 289-307.

- Numerical investigation of D-bifurcations for a Stochastic Delay Logistic Equation, Stochastics and Dynamics 5 (2005) 211-222.
- Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations Communications in Pure and Applied Analysis, 5 (2006) 367-382.
- Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochtastic delay differential equations. Accepted, to appear in Proceedings of Algorithms for Approximation V.

- A genetic-algorithm approach to simulating human immunodeficiency virus evolution reveals the strong impact of multiply infected cells and recombination. J. General Virology 86 (2005) 3109-3118.

- Bifurcations in approximate solutions of stochtastic delay differential equations, International Journal of Bifurcation and Chaos 14 (2002) 2999-3021

- Numerical modelling by delay and Volterra functional differential equations, Computer Mathematics and its Applications (2006) 233-256.

- Simulation of grain boundary creep: analysis of some new numerical techniques, Proceedings of the Royal Society of London, Series A 460 (2004) 2395-2413.

- Determining control parameters for dendritic cell-cytotoxic T lymphocyte interaction. Eur J. Immunol 34 (2004) 2407-2418

- A Mathematical Approach for Optimizing Dendritic Cell-Based Immunotherapy. In: Adoptive Immunotherapy. Methods and Protocols, Eds Ludewig B and Hoffmann M.W. (Humana Press) (2004).

- Solution map methods for stability analysis of linear and nonlinear Volterra difference equations, International Journal of Applied Science and Computations 11 (2004) 35-52.

- Flexible parallelization of fast wavelet transforms, Parallel Algorithms and Applications 18 (2003) 155-169

- Mathematics Teaching/Learning in HE
- Progressive introduction of computer software in the undergraduate mathematics curriculum (proceedings of the International
- Conference on Technology in Mathematics Teaching, Birmingham 1993.
- Linear Algebra with PC Matlab, Maths & Stats, February 1993
- Software Tools: From doing to thinking? Maths & Stats, February 1994

- Local area micronetworks and their management, NCC, 1989
- BASIC Applications, NCC Blackwell, 1990
- Computer Programming Languages, Ellis Horwood, 1990

- Computers and Computer Applications, Ellis Horwood, 1991 5.

Introducing Formal Methods, Ellis Horwood, 1993 (with M Woodroffe) Introducing Software Engineering, Prentice Hall, 1994