Current Research Projects

Surface fitting with application to plant architectures

Gradient Estimation from discrete function values

Functional Structural models of Macadamia

Mathematical modelling of digestive processes

Recent Projects 

Modelling protein recruitment and expulsion in endosomal systems

Stochastic algorithms for Optimisation.

A multidimensional integral equation - numerical solution by iteration based on physical arguments

Parameter fitting for the Climex software program

Investigation of the teaching of linear algebra to tertiary students

Co-authored two volumes on Senior Mathematics B with R.Boggs, K. Bolger, and R. Farragher.

Research Awards 

2010  ARC Linkage grant.  $440,000, 2010-2012  Partners  Prof. Ian Turner, QUT, Dr, Scott McCue, QUT, Dr. J Hanan , UQ, Dr.Gary Dorr, UQ,  Dr . G .Elliot, ANU,  Dr Alison Forster, Plant Protection Chemistry, New Zealand, Dr. Jerzy Zabkiewicz, Plant Protection Chemmistry, Nre Zealand, Nufarm Australia, Syngenta Crop Protection.

2004  Parameter fitting for the Climex software package   $10,000  CSIRO division of Entomology

1.  Mathematics for Queensland  Year 11B . K. Bolger, R. Boggs, R.Faragher, J.A.Belward.  Oxford University Press, Melbourne 2001,
ISBN 0 19 550852.  

2. Mathematics for Queensland  Year 12B . K. Bolger, R. Boggs, R.Faragher, J.A.Belward.  Oxford University Press, Melbourne 2002,
ISBN 0 19 550853.

Research Papers

1. The solution of a Fredholm integral equation of the first kind. Quarterly of Applied Maths., 27 (1969), pp. 313-321.

2. Solutions of some Fredholm integral equations using fractional integration, with an application to a forced convection problem. Z.A.M.P., 23 (1972), pp. 901-917.

3. Forced Convection problems and some related integral equations. Ph.D. thesis abstract. Bull. Austral. Math. Soc., 6 (1972), p.471.

4. Elastic waves in a prestressed Mooney material. Bull.Austral.Math. Soc. 7 (1972), pp. 153-161.

5. Some dynamic properties of a prestressed incompressible hyperelastic material. Bull. Austral. Math . Soc. 8 (1973), pp.61-74.

6. On the relationship of some Fredholm integral equations of the first kind to a family of boundary problems. J. Math. Anal. and Applics 48 (1974), pp. 184-199.

7. An axially symmetric forced convection problem. J. Austral. Math. Soc. 20 (1975), pp. 1-17.

8. The propagation of small amplitude waves in prestressed incompressible elastic cylinders Int. J. Engng. Sci. 14 (1976), pp. 647-659.

9. An integral equation solution for the plane strain of a fibre reinforced ellipse. J. Comp. Phys. 42 (1982), pp. 215-236.

10. Further solutions of a Fredholm integral equation of the first kind arising in elastic half space and forced convection problems. Quart. J. Mech. and Appl. Maths. 36 (1983), pp. 237-245.

11. Further studies of the application of constrained minimisation methods to Fredholm integral equations of the first kind. I.M.A.J. Num. Anal. 5 (1985), pp. 125-139.

12. Existence of solutions of Oseen type integral equations. Bull.Austral. Math. Soc. 29 (1984), pp. 57-66.

13. Nonlinear least squares - theory, algorithms and software. Presented at the Sixth Joint Summer School ``Advances in Numerical Algorithms'', Manchester 1984. An invited paper published in the Summer School proceedings, Numerical Algorithms, edited by J.L.Mohamed and J.Walsh, pp. 275-292Clarendon Press, Oxford, 1986.

14. An exponential version of Filon's rule. J. Comput. and Appl. Maths. 14 (1986), pp. 461-466.

15. Numerical solutions of the compressible flow Oseen integral equation. Computational Techniques and Applications: CTAC---89. Eds. W.L.Hogarth and B.J.Noye, Hemisphere Publishing, New York , 1990.

16. Propagation of waves in cylinders of incompressible materials; modes with complex wave numbers. Quart. J. Mech. and Appl. Maths. 40 (1987), pp. 383-399. (Joint with S.J.Wright).

17. Computers and contemporary Mathematics. ( An invited paper) Q.A.M.T. Journal 13 (1988), pp. 21-27.

18. Searching for Solutions - Experimental Applied Mathematics in a Primary Environment. In Proceedings of the 9th Computers in Education conference, 1991, pp. 231-244. ,Research and presented at the Annual of the Australian Computers in Education Conference at Bond University in September 1991.

19. Damping of Resonances in Rectangular Radio Frequency and Microwave Packages
and Module Housings.  I.R.E.E.convention, Sydney, September 1991.  Joint with J.A.R.Ball and T.Downs,

20. The solution of Fredholm integral equations on transputer arrays, Applications of Transputers 3, Vol. I, IOS Press, Amsterdam,(1991), pp. 93-98.

21. Multi-Processor Algorithms for Fredholm Integral Equations . in Transputing for Numerical and Neural Network Applications, published in Amsterdam, by IOS Press, in the Transputer and Occam Series, 1992, pp. 110-122. Edited by G.L.Reijns and J. Luo, Delft Technical University, NL.

22. A Variational Approach for the Histogram Modification of an Image, Proceedings of the 5th Australian Transputer and Occam User Group Conference, 4-5 November 1992, Melbourne, Australia, IOS Press, 1993, pp. 1-6.( Joint work with I.Altas , and J. Louis)

23. Drought Monitoring through Parallel Computing. Proceedings of the Sixth SIAM Conference on Parallel Processing in Scientific Computation pp. 117-12.. Edited R. Sincovec et al. Published by S.I.A.M. Press, Philadelphia 1993.( Joint work with K. Burrage, F. Duncalfe, R. Young, L.Lau, and M.Rezny).

24. Computers in Mathematics A, B, and C, Teaching Mathematics, 17, 1992, pp 39-41.

25. Tank Calibration - Practical Examples in Approximation. The UMAP Journal, 15 , No. 1, pp 29-42, 1994.

* 26. A New Image Enhancement Algorithm on MasPar and Parallel Virtual Machine (PVM) Environments, in the proceedings of the 1994 EUROSIM Conference on Massively Parallel Processing Applications and Development, Delft, Holland (1994) pp. 819 - 826. (Joint work with J.Louis, I.Altas, R.Moore, K.Burrage and M.Rezny).

27. A variational approach to the Radiometric Enhancement of Digital Imagery I.E.E.E Transactions on Image analysis, 4, No. 6, pp 845-849, 1995. (Joint work with J. Louis, and I.Altas).

28. ADVISE Agricultural Development Visualisation Interactive Software Environment Presented at the CONPAR meeting, Linz, Austria, September 1994. (Joint work with L.Lau, I.Altas,  K.Burrage and M.Rezny).

29. Tau Method Approximations for the Bessel Function Y₀(z). Computers Math. Applic. 30, pp 5-14, 1995. (Joint work with J.Zhang).

30. Simulated annealing - a robust optimisation technique for fitting nonlinear regressions. IASTED. Conference on Modelling, Simulation and Optimisation , Gold Coast, 1996. (Joint work with K.Burrage, P.M.Pepper and D.G.Mayer).

31. Use of Advanced Techniques to Optimise a Multi-Dimensional Dairy Model. Agricultural Systems, 50, pp 239-253, 1996  (Joint work with K.Burrage and D.G.Mayer).

32. A Stochastic Simulation of Sintered Microstructures. In Sintering Technology, eds German, Messing, Cornwall, pp 365-372. Published by Marcel Dekker, New York, 1996.(Joint with G.B.Schaffer, T Sercombe, K. Burrage, and I. Podolsky.)

33. Monitoring the knowledge of entrants to First Year Engineering at the University of Queensland. pp. 695-704, in The Role of Mathematics in Modern Engineering, eds. A.K.Easton and J.M.Steiner. Student Literatur, Lundberg April 1996.

34. Optimisation of a dairy farm model - Comparison of Simulated Annealing, Simulated Quenching, and Genetic Algorithms. Proceedings of International Conference on Modelling and Simulation, pp33-38. Vol.1. Eds. Binning,P., Bridgman,H., Williams, B. November 1995. (joint with D. Mayer, K. Burrage, and M.A.Stuart)

35. An Image Enhancement Algorithm on Parallel Virtual Machine (PVM) Environment. Journal of Mathematical Sciences, 7, pp. 53-63, 1996 . (Joint with Altas, I., Rezny, M., Louis, J., Burrage, K., and Moore, R. ) .

36. The Multi-Faceted Challenge of Teaching University Mathematics at the Close of the 20th Century. In Proceedings of Second State Conference of HERDSA (inc.) Qld on ‘Student Diversity in Higher Education; Implications for Teaching and Learning. University of Southern Queensland April13-14 1996. On disc.

37. Coupling Spatial Models at Varying Space and Time Scales. MODSIM 97, International Conference on Modelling and Simulation Proceedings, 1997. Volume 2, pp. 669-674. J.A. Belward, K.Brook, G.McKeon, R.Young, L.Lau. (A)

38. Fractal Dimensions for Rainfall Time Series. MODSIM 97, International Conference on Modelling and Simulation Proceedings, 1997. Volume 1, pp. 48-5  Joint with M. Breslin. 

39. Use of Evolutionary Algorithms and Simulated Annealing to Optimize
a Herd Dynamics Model. MODSIM 97, International Conference on Modelling and Simulation Proceedings, 1997. Volume 3, pp. 1109-1114. Joint with D.G. Mayer and K. Burrage

40. A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. BIT 1997, 37, pp771-780. Joint with P. Burrage and K. Burrage.

41. Chebyshev Series Approximation for the Bessel Function Yn(z) of Complex Argument Applied Mathematics and Computation. Vol. 88 (2-3), pp. 275-286 (1997). Joint with J. Zhang.

42. Optimizing simulation models of agricultural systems. Annals of Operations Research. Vol. 82, 1998, pp. 219-231. Joint with D.G.Mayer and K.Burrage.

43. Tabu Search Not an optimal Choice for Models of Agricultural Systems. Agricultural Systems, 58, no.2, 243-251, 1998. Joint with D.G.Mayer and K.Burrage.

44. Survival of the fittest - genetic algorithms versus evolution strategies in the optimization of systems models. Agricultural Systems, 60, no. , pp113-122, 1999. Joint with D.G. Mayer, H.Widell, and K. Burrage.

45. Fractal Dimensions for rainfall time series. Mathematics and Computers in Simulation, 48, nos. 4-6, pp437-446, 1999. Joint with M.C.Breslin .

46. Performance of Genetic Algorithms and simulated annealing in the economic optimization of a herd dynamics model. Environmental International, 25, nos.6/7, pp899-905, 1999.  Joint with D.G. Mayer

47.  Survival of the fittest - Genetic algorithms versus evolution strategies in the optimization of systems models.Agricultural Systems  60 1999 pp 113-122 (D.G.Mayer, J.A.Belward, H. Widell and K.Burrage.)

48.  More reform needed yet… The Challenge of Diversity -  Proceedings of the Delta 99 symposium on undergraduate mathematics. Published by the Delta 99 committee, ISBN 0 646 38371 X  1999,    pp33-37.

49.Robust parameter settings of evolutionary algorithms for the optimisation of agricultural systems models  Agricultural Systems  69 2001 pp99-213 (D.G.Mayer, J.A.Belward and K.Burrage.)

50. Short term forecast of the load demand in Victoria . MODSIM 2001, International Conference on Modelling and Simulation.  Volume 3, 2001,  pp.1065-1070,  ISBN 0-867405252  Joint with C Baloi,  M Bulmer.

51.   Numerical Algorithms - enhancing presentation while maintaining rigour in introductory courses: A minimalist approach to course modernization.  Refereed conference paper presented at ICTM2,  Crete,July 2002. Published by J.Wiley & Sons. ISBN 0-471-46332-9.  http://www.math.uoc.gr/~ictm2/Proceedings/pap258.pdf

52.  Boundary treatment for Virtual Leaf Surfaces.   GRAPHITE 2003, Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, Melbourne, Australia. pp. 261 - 262,  2003,   ISBN:1-58113-578-5  joint with B.I.Loch and J.S.Hanan.

53  .Sensitivity Analysis Of The National Electricity Market,    Proceedings of MODSIM 2003  International Conference on Modelling and Simulation Editor D.A.Post  Townsville Australia, July 2003.  pp.1084 - 1089,  ISBN 1 74052 096 X.      Joint with C. A. Baloi and M. Bulmer.

54 . Genetic Unit Commitment Model In A Deregulated Power Energy Environment.  Refereed proceedings of MODSIM 2003  International Conference on Modelling and Simulation Editor D.A.Post  Townsville Australia, July 2003.  pp. 1078 - 1083.  ISBN 1 74052 096 X.      Joint with C. A. Baloi and M. Bulmer

55.  Multi - Area Unit Commitment In The National Electricity Market .   Proceedings of MODSIM 2003  International Conference on Modelling and Simulation Editor D.A.Post  Townsville Australia, July 2003  pp1685 - 1690.  ISBN 1 74052 096 X.      Joint with C. A. Baloi and M. Bulmer

Successful Higher Degree Candidates

1981 M. J. Flaherty "Time-frequency analysis of speech via modulated splines".

1984 S.H.Masood "Attenuation and propagation of axisymmetric stress waves through rubber cylinders"

1988 J.A.R.Ball "A dyadic Green’s function for microstrip enclosures"

1992 J.A. Young "On the optimal expansion of Electric Power Systems"

1995 M.Rezny "Aspects of High Performance Computing"

1999 Pamela Burrage "Runge-Kutta Methods for Stochastic Differential Equations"

2000 D.G.Mayer "Optimisation of Agricultural Production Systems"

2001 Monique C. Breslin "Mathematical modelling applied to long term climate analysis"

2003  Brian Eadie "Prediction of Rock Fragmentation under Caving" joint with E.T. Brown

2003  Cristian A.Baloi "Applications of Forecasting and Optimisation in the Australian National Electricity Market"

2009 Moa'ath Oqielat   " Modelling Water Droplet Movement on a Leaf Surface"  joint with I.W.Turner.

Personal history

Ph.D. thesis title: Forced Convection Problems and Some Related Integral Equations of the First Kind . Supervised by A.F.Pillow and V.G.M.Hart. Degree approved in January 1972. (An abstract appeared in Bull. Austral. Math. Soc., 6, 1972, p.471)

Positions held:

JULY 1959-NOVEMBER 1961. Performance Engineer for Joseph Lucas (Gas Turbine Equipment) Ltd., Birmingham. (Duties largely involved servomechanism analysis and analogue simulation of electronic and hydraulic aircraft engine control systems.)

NOVEMBER 1961-JUNE 1964. Assistant Lecturer in the Department of Mathematics at the University of Aston.

JULY 1964 - JANUARY 2003. Lecturer (1964-1973), Senior Lecturer (1974 - 1993), and Reader (1994- 2003) in Mathematics at the University of Queensland, Brisbane, Queensland, Australia.

JANUARY 2003.  Honorary Reader, Advanced Computational Modelling Centre, University of Queensland

FEBRUARY 2004.  Casual Lecturer,  MAB312. Queensland University of Technology,  School of Mathematics.

 FEBRUARY 2004.  Educational Consultant , QUT.

Queensland University of Technology e-mail:  j.belward@qut.edu.au