Home Page for Professor Christopher T H Baker

School of Mathematics

The University of Manchester,

Manchester, M13 9PL, United Kingdom

Home Page for Christopher Baker

Professor Emeritus, School of Mathematics, The University of Manchester [Alan Turing Building Room 1.217]

Professor, part-time, Mathematics Dept., The University of Chester [Tower, Room 7.02]

Christopher Baker no longer undertakes formal teaching but pursues research activities.

Contact:

Email: cthbaker[at]na-net.ornl.gov, christopher.baker[at]manchester.ac.uk, c.baker[at]chester.ac.uk

Phone: [Chester] +44 1244 51 1460

Phone: [Manchester] +44 161 30 6360 email Christopher.Baker@manchester.ac.uk (Dept: +44 161 275 5800)

Fax: [Manchester] +44 161 275 5819 [Supplement any fax with an E-mail]

Causal problems, Volterra integral and integro-differential equations, delay differential equations, retarded differential equations, difference equations, summation equations, numerical solution, computational models in mathematical biology, identification, inverse problems, … .

 Christopher Baker: Educated at Colchester Royal Grammar School (1951--58)

and at Jesus College, University of Oxford: College Scholar (1958--61); BA (1961); M.A., D.Phil. (1964).

Forthcoming meetings in which I am to be involved

Leverhulme stochastic network, Chester: Numerical and analytical solution of stochastic delay differential equations, 7th to 10th September 2009, University of Chester. http://www.stochasticdelay.org.uk/index.html

First International Workshop on Differential and Integral Equations with Applications in Biology and Medicine , 7th to 10th September, 2010. http://www.icsd.aegean.gr/diebm2010

Current Research Interests

Key words Analysis, numerical analysis & modelling-- particularly in bio-mathematics: Volterra integral and integro-differential equations, deterministic & stochastic delay and neutral equations; model selection & inverse problems.

· Numerical solution of functional differential equations (integro-differential equations and deterministic and stochastic delay-differential equations [D and S DDEs]); evolutionary problems with after-effect.

· Applications and parameter estimation in models (e.g., cell proliferation) ; Inverse problems

· Numerical solution of integral equations

· Numerical simulation in Biomathematics etc.; Scientific computation & codes

Books

· Numerical Treatment of Integral Equations, Clarendon Press, Oxford 1977 (reprinted 1978)

· The Numerical Solution of Nonlinear Problems, Clarendon Press, Oxford, 1981 (editor, with C. Phillips)

· The Treatment of Integral Equations by Numerical Methods, Academic Press, London, 1982 (editor, with G. F. Miller). 

Christopher T H Baker: Research

Papers – a selection

Click the link here to examine selected output. [username PUBLICATIONS, enter PASSWORD]

Papers published between 2001 and early 2008 – itemised (most recent first).

>      Baker, C. T.H.  & Parmuzin, E. I., Initial function estimation for scalar neutral delay differential equations
 Russian J. Numer. Anal. Math. Modelling, Volume 23, No.2 (2008) pp 163—183.

http://www.reference-global.com/doi/pdf/10.1515/RJNAMM.2008.010

>      Baker C T H,  Bocharov G, Parmuzin, E., Rihan F Some aspects of causal & neutral equations used in modelling
Journal of Computational and Applied Mathematics, In Press, Corrected Proof, Available online 8 April 2008

>      Andrew S.M., Baker C T H & Bocharov  G A Rival approaches to mathematical modelling in immunology J. Comput. Appl. Math, (2007) 669-686 DOI: 10.1016/j.cam.2006.03.035

>      Baker C T H,  Bocharov G, Filiz A, Ford N, Paul C, Rihan F, Thomas R M, Tian H & Willé D R
Numerical Modelling by delay and Volterra functional differential equations pp 233-256   in Computer Mathematics and its Applications Advances and Developments (1994-2005) (E A Lipitakis, editor) LEA Publishers, Athens, Greece  2006. ISBN 960-87275-9-6. http://www.aueb.gr/pympe/hercma/books/CMA-AD-COVER-ADV-1.doc

>        Baker C T H & Lumb P M, On integral equation formulation of a class of evolutionary equations with time-lag. J. Integral Equations and Applications. 18 (2006) 227-248 http://rmmc.eas.asu.edu/abstracts/jie/vol18-2/contents.pdf

>       Baker, C T H, Agyingi, E O, Parmuzin, E I, Rihan, F A, & Song, Yihong, Sense from sensitivity and variation of parameters,  Appl. Numer. Math 56 (2006), 397--412.  DOI:10.1016/ j.apnum.2005.04.007

>        Baker, C T H  &  Paul, C A H  Discontinuous solutions of neutral delay differential equations, Appl. Numer. Math. 56 (2006), 284-304. DOI:10.1016/ j.apnum.2005.04.009

>        Baker, C T H & Bocharov, G A, Computational aspects of time-lag models of Marchuk type that arise in immunology, Russian Journal of Numerical Analysis and Mathematical Modelling, 20 (2005) 247-262. DOI: 10.1163/1569398054308630 http://www.ingentaconnect.com/content/vsp/rjmm/2005/00000020/00000003/art00003

>        Baker, C T H.  & Buckwar, E.  On Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations, Stochastics and Dynamics 5 (2005) 201-209.

>        Baker, C T H  & Buckwar, Evelyn,   Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations.  J. Comput. Appl. Math, 184 (2005) 404-427  DOI: 10.1016/j.cam.2005.01.018

>        Baker, C. T.H.  & Parmuzin, E. I., Identification of the initial function for discretized delay differential equations, J. Comput. Appl. Math., 181 (2005) 420-441. DOI: 10.1016/j.cam.2004.11.035

>       Baker, C. T.H.  & Parmuzin, E. I., Identification of the initial function for nonlinear delay differential equations, Russian J. Numer. Anal. Math. Modelling, 20 (2005) 45-66.  DOI: 10.1163/1569398053270831 

http://www.ingentaconnect.com/content/vsp/rjmm/2005/00000020/00000001/art00003

>       Baker, C.T.H., Bocharov, G.A., Paul, C.A.H., Rihan, F.A., Computational modelling with functional differential equations: identification, selection and sensitivity, Appl. Numer. Math., 53 (2005) 107—129 DOI: 10.1016/j.apnum.2004.08.014

>       Baker C T H, Bocharov G A, Ford J M, Lumb PM, Norton SJ, Paul CAH, Junt, T., Krebs, P., Ludewig, B., Computational Approaches to Parameter Estimation and Model Selection in Immunology .  J. Comput. Appl. Math., 184 (2005) 50-76. DOI: 10.1016/j.cam.2005.02.03

>     Baker C T H & Parmuzin E I, Analysis via integral equations of an identification problem for delay differential equations, J Integral Equations Appl. 16 (2004) 111-135. http://rmmc.eas.asu.edu/abstracts/jie/vol16-2/contents.pdf

>        Song, Yihong & Baker C T H, Qualitative behaviour of numerical approximations to Volterra integro-differential equations, J. Comput. Appl. Math., 172 (2004) 101-115. DOI:10.1016/j.cam.2003.12.049

>     Baker C T H & Song, Yihong, Periodic solutions of discrete Volterra equations, Math. Comput. Simul. 64 (2004) 521-542.DOI:10.1016/j.matcom.2003.10.002

>     Song, Yihong, & Baker CTH, Perturbation of Volterra differemce equations, J. Difference Equa. Appli. 10 (2004) 379-397. DOI:10.1080/10236190310001625253

>    Song, Yihong  & Baker CTH, Linearized stability analysis of discrete Volterra equations, J. Math. Anal. Appl., 294 (2004) 310-333.  DOI:10.1016/j.jmaa.2004.02.019

>     Baker CTH, Ford JM & Ford NJ,  Bifurcations in approximate solutions of stochastic delay differential equations, International Journal of Bifurcation and Chaos 14 (2004) 2999-3021  DOI:10.1142/S0218127404011235

>      Baker C T H & Song, Yihong, Discrete Volterra operators, fixed point theorems and their application, Nonlinear Stud., 10 (2003) 79-101. ISSN 1359-8678 http://www.nonlinearstudies.com/

>     Song, Yihong & Baker C T H, Perturbation theory for discrete Volterra equations, J. Difference Equ. Appl., 9 (2003) 969-987. DOI:10.1080/1023619031000080844

>     Baker, C T H., Paul,C.A.H. & Tian, Hongjiong, Differential algebraic equations with after-effect, J. Comput. Appl. Math., 140 (2002)

63-80.NO doi:

>        Baker C T H, Bocharov G A, Filiz A, Ford N J, Paul C A H, Rihan F A, Tang A, Thomas R M, Tian H & Willé D R, Numerical modelling by retarded functional differential equations, Hellenic European Research on Mathematics and Informatics Science  Vol 2, (2001) 29-52. ISBN: 960-85176-7-2

>        Baker, C T H., A perspective on the numerical treatment of Volterra equations, pp. 217--249 of Baker C., Monegato G, Pryce J & Vanden Berghe G (eds)  Numerical analysis 2000. Vol. 6: Ordinary differential equations and integral equations. Elsevier Science Publishers, B.V., Amsterdam, 2001; 540 pp. ISBN 0-444-50600-4

>        Baker, C T H., Retarded differential equations, pp. 309-335 of   Baker C., Monegato G, Pryce J & Vanden Berghe G (eds)  Numerical analysis 2000. Vol. 6: Ordinary differential equations and integral equations. Elsevier Science Publishers, B.V., Amsterdam, 2001; 540 pp. ISBN 0-444-50600-4

>        Baker, C T H., A perspective on the numerical treatment of Volterra equations, pp415-447 of C. Brezinski, L. Wuytack (eds) Historical Developments in the 20th Century, Elsevier Science Publishers, B.V., Amsterdam, 2001, ISBN 0-444-50617-9 (and  see above)

>        Baker, C T H., Retarded differential equations, pp479-505 of C. Brezinski, L. Wuytack (eds) Historical Developments in the 20th Century, Elsevier Science Publishers, B.V., Amsterdam, 2001, ISBN 0-444-50617-9 (and  see above)

>        Baker, C. T. H.; Willé, D.R.: On the propagation of derivative discontinuities in Volterra retarded integro-differential equations. Dedicated to John Butcher. New Zealand J. Math. 29 (2000), 103--113.

>        Baker, C. T. H.:  Retarded differential equations. J. Comput. Appl. Math. 125 (2000),  309--335. (and  see above)

>        Baker, C. T. H.: A perspective on the numerical treatment of Volterra equations J. Comput. Appl. Math. 125 (2000), 217—249  (and  see above)

>        Baker, C. T. H., Buckwar, E.:  Numerical analysis of explicit one-step methods for stochastic delay differential equations. LMS J. Comput. Math. 3 (2000), 315—335

>        Baker, C. T. H., Buckwar, E.:  Continuous $\Theta$-methods for the stochastic pantograph equation. Electron. Trans. Numer. Anal. 11 (2000), 131—151

>     Ford, N.J., Baker, C. T. H.:  Preserving transient behaviour in numerical solutions of Volterra integral equations of convolution type. Integral and integrodifferential equations, 77--89, Ser. Math. Anal. Appl., 2, Gordon and Breach, Amsterdam, 2000.

>        Baker, C. T. H., Tang, A. : Generalized Halanay inequalities for Volterra functional differential equations and discretized versions. Volterra equations and applications, 39--55, Stability Control Theory Methods Appl., 10, Gordon and Breach, Amsterdam, 2000.

Some Professional Activities:

On the following academic reviews (most recent)

o Quality review, Mathematics Dept, Dublin City University, 2006

· CWI research institute Amsterdam, 2005

· Chairman, Applied Mathematics Panel (Unit of Assessment 23) HEFCE Research Assessment Exercise (RAE) 2001

· Member, HEFCE Research Assessment Exercise (RAE) Applied Mathematics Panel 1996.

· Member,HEFCE

Research Assessment Exercise (RAE) Mathematics Panel 1992

o Member of EPSRC Peer Review College [continuing since its inception].

On the Editorial Board of: Journal of Computational Applied Mathematics

Honorary Editor, Communications on Applied Nonlinear Analysis

Past editorial duties (journals):

Guest Editor: Annals of Numerical Mathematics volume 1.

Guest Editor Volume 6, (Delay and Volterra Equations), Millenium Issue of Journal of Computational Mathematics 2000.

Journal of Integral Equations (from inception 1979 to demise in 1987)

IMA Journal of Numerical Analysis (from inception to 1996)

Advances in Computational Mathematics (from inception to 2002)

Journal of Integral Equations and Applications (from inception in 1989 to May 2003)

Guest Editor, Special Issue on Evolutionary Problems,, Journal of Computational Mathematics 2007 [Volume 205, Issue 2, 15 August 2007]

Guest Editor, Proceedings IWANASP2006, Journal of Computational Mathematics 2008 (in press)

Past Symposia Organized:

o Convenor, LMS-SERC Durham Symposium on Numerical Treatment of Integral Equations

· Convenor, LMS-EPSRC Durham Symposium on Evolutionary Problems

Was on the Scientific Committee for:

o The State of the Art in Numerical Analysis Conference, April 1996, York.

· Computational Applied Mathematics (Leuven) -- biennially

· Hermis Meeting, Athens, etc.

· Meeting in tribute to Professor  Myskhis  (Russia, 2000)

· BAMC  2000, etc.

Society Membership, etc.:

o Member of LMS (London Mathematical Society)

· Member  (reappointed 2000;  further reappointed 2002, then 2006-- ) of EPSRC Mathematics College

· . . .

· quandam Member of the LMS Durham Symposia Committee

· quandam Fellow of IMA, C.Math.

· quandam Member of SIAM (Society for Industrial & Applied Mathematics)

· quandam Member, and then (1996-7) Chairman, Fox Prize Adjudicators

Some Previous Co-authors: 

S. Amini, P.M. Anselone, H. Arndt, J.C. Butcher, G. Bocharov, E.Buckwar, M.S. Derakhshan, A.Filiz, N.J.Ford, J.M.Ford, G.S. Hodgson, P.van der Houwen, V. Kolmanovskii, P.M.Lumb, A. Makroglou, E Parmuzin, C.A.H. Paul, P.A. Radcliffe,  P.Lumb, S.Norton, F.A.Rihan, E. Short, B. Sommeijer, Y. Song, A. Tang,  R.M.Thomas, H.J.Tian, D.R. Wille, P.H.M. Wolkenfelt, etc.

A Selection of Conference Talks &tc:

Christopher Baker          … at a conference lecture.  

o Invited plenary talk, Athens, September 1998

· Invited plenary talk  (the "mystery " guest speaker  --- as a surprise for John Butcher) Auckland, December, 1998

· 60^th Birthday Seminar, UMIST-University of Manchester, Jan 20th 1999

· A talk in the Minisymposium at ICIAM99 (Edinburgh) [Two sessions (jointly organised with Dr Neville Ford)], MSP-036 11.00-13.00 on Tuesday 6th July and MSP-072 16.00-18.00 on Tuesday 6th Jul 1999.

· A talk in the Minisymposium at SciCADE99 (Queensland) [Two sessions (jointly organised with Prof Alfredo Bellen)], August 1999.

· A talk at ANODE99 (Auckland) August 1999.

· Invited 45 min talk, AMS meeting Washington, 19-22nd Jan 2000, ( AMS Special Session on Integral Equations and Applications, III ),

· BAMC Minisymposium on Causal Problems (UMIST April 2000)

· Further invited conference talks:

§ ICCAM2000, Leuven July 17-21st 2000 (17th July 2000--plenary),

· Nonlinear Analysis, Catonia, 19-26th July 2000 (at 2 minisyposia).

· IMACS Lausanne  Aug 2000 (minisymposium on delay equations)

· …..

· Second meeting on singular problems, Samos, Sept. 2006

^{Past & Present University Commitments}

o Previous appointments at University of California at Berkeley, and University of Toronto.

· Visiting Professor of Applied Mathematics at Chester College (Current)

· University Research Professor in the University of Manchester (Sept 30^th 2001 to Sept 30^th 2004)

· Professor Emeritus, University of Manchester  (from September 1^st 2004)

· Founding Director of Manchester Centre for Computational Mathematics (This Center ceased to exist on the demise of the Victoria University of Manchester.)

· Former Member of Dean's Advisory Committee (Faculty of Science & Engineering  (The Victoria University of Manchester).

· Formerly: ex officio Member, Faculty of Science and Engineering (The Victoria University of Manchester) Member, Faculty of Arts (The Victoria University of Manchester).

· Formerly: ex officio Member of Senate until its reconstitution in 2000 (The Victoria University of Manchester).

· Formerly: appointed  Senate member of Joint Committee on University Development  unitl Senate reconstituted in 2000 (The Victoria University of Manchester).

· quandam Member of University Court. (The Victoria University of Manchester).

· Formerly: Member of Faculty Development Sub-committee (1995-1998) (The Victoria University of Manchester).

· Formerly: Head of Department of Mathematics, Pure and Applied, (1995-1998)

Christopher T H Baker

This page is maintained by Christopher Baker
(cthbaker@ma.man.ac.uk): Modified 
05-06-08