| Prof. John C. Butcher
(
紐西蘭皇家科學院院士 )
Some New Methods for Stiff and Non-stiff Problems
摘要
| | Abstract:
General linear methods were introduced to provide a theoretical framework to study vastly different methods within a single formulation.It is now realized that they have more than this abstract significance and some new classes of practical algorithms have been found using this approach.In this lecture, some of the limitations of existing methods will be discussed and general linear methods will be introduced which do not suffer these limitations to the same extent.The key idea is known as "Runge-Kutta stability" and expresses the property that, from a stability point of view, the new methods behave every much like Runge-Kutta methods. On the other hand they have clear-cut advantages over standard Runge-Kutta methods. |
91年4月22日 (星期一)
下午15:10-16:00
台灣大學數學系新數館308室
Aim of the
visiting
| Prof. J.C. Butcher is a famous scholar in the field of Numerical analysis.His early works establish the fundamental basis in the theory of numerical Analysis for O.D.E. The so-called Butcher theory, Butcher series, Butcher tree,
Butcher barrier etc, are the main part of the study in the history of the numerical method: Runge-Kutta methods. No doubt, he is a pioneer in this field.
Prof. J.C. Butcher is not only a Ph.D. (Sydney, Australia), but also a D.Sc. (Doctor
of Science, Sydney, Australia). He has been award number of medals and prizes. He is a fellow of Royal Society, New Zealand. (紐西蘭皇家科學院院士).His publications are over 100 (refer to http://www.math.auckland.ac.nz/~butcher) His research works always drew a lot of attention not only in the field of numerical analysis, but also in the field of theoretical physics. Recently, he devoted himself to seek some practical numerical methods for stiff differential equations which play an important role in practical application. Some results obtained by Prof. J.C. Butcher are crucial and effective. The contents of his talks (abstracts of the talks are attached) is expected to include
(1)Review the Runge-Kutta methods for the past one decade
(2)The fundament theory of Runge-Kutta methods
(3)The practical Runge-Kutta methods
After these talks and his visiting, the aims are as follows:
a.From these talks, we will learn the history of the numerical methods and realize how this study goes for the last one hundred years. We will know many crucial aspects in the field of numerical analysis and how to deal with some difficulties in the near future. It is also expected that we can understand what is the fundamental theory in the field of Numerical Analysis for O.D.E.
b.Prof. Butcher is also an editor of many famous journals (SCI). He organized quite a few international conferences around the world. It is expected that we can take the advantage of his visiting to arise the status of Taiwan.
c.These talks will inspire the local researchers in the study of numerical analysis, especially in Computational Mathematics which is getting more important in the branch of Mathematics. |
Schedule of the visiting
|
訪問時間 |
訪問地點 |
工作要項 |
|
4月22日 (一)
PM 3:00- 5:00 |
台灣大學數學系
(與中央研究院數學所合辦) |
演講、訪問、指導研究生 |
|
4月24
日(三)
PM 1:00- 3:00 |
嶺東技術學院 |
演講、訪問 |
|
4月29日 (一)
AM 9:00-12:00 |
清華大學
(國家理論科學研究中心) |
演講、訪問、指導研究生 |
|
5月1日(三)
PM:3:30-5:30 |
中正大學數學系 |
演講、訪問、指導研究生 |
Biography of John C.
Butcher
| Born
31 March 1933
Auckland, New Zealand
New Zealand citizen
Present Position
Honorary Research Professor, Department of Mathematics, The University of Auckland
Research Insterests
Numerical methods for the solution of ordinary differential equations
Education
University of New Zealand (Auckland University College), 1952-1955; B.Sc, 1955.
University of New Zealand (Auckland University College), 1956; M.Sc, 1956.
University of Sydney, 1956-1960; Ph.D, 1961.
University of Sydney, 1971, D.Sc, 1971
Positions held
Lecturer, University of Sydney, 1959-1961.
Senior Lecturer, University of Canterbury, 1961-1964.
Computer Scientist, Stanford Linear Accelerator Center, 1965-1966.
Professor of Mathematics, University of Auckland, 1966-1979.
Head of Mathematics Department, University of Auckland, 1967-1973.
Founded Department of Computer Science, University of Auckland, 1980.
Professor of Computer Science, University of Auckland, 1980-1988.
Head of Applied and Computational Maths Unit, University of Auckland, 1989-1994, 1997-1998.
Professor of Mathematics, University of Auckland, 1989-1998.
Honorary Research Professor, 1999- .
Memberships
Elected Fellow, Royal Society of New Zealand, 1980
Member and Past President New Zealand Mathematical Society
Society for Industrial and Applied Mathematics
Australia and New Zealand Industrial and Applied Mathematics
Awards
Award for Mathematical Research, NZ Mathematical Society, 1991
For establishing new fundamental connections between analytic stability properties and algebraic properties of numerical methods for non-linear differential equations; for implementing new methods; and for an outstanding monograph on Runge-Kutta and general linear methods.
Hector Memorial Medal, Royal Society Of NZ, 1996
For research in the Numerical Analysis of Differential Equations.
Visiting Positions and Conferences
1970 Various British Universities (few days each) Royal Institute of Technology, Stockholm,Sweden (one week) Innsbruck, Austria Unvited Speaker, 400th anniversary, Universitat Innsbruck (one week) Prof a l'ecole d'ete, Breau-sans-Nappe, France (3 weeks)
1972 Dundee, Scotland (8 months) Vienna, Austria (4 months)
1979 Linkoping, Sweden, visiting Professor (several months) Bonn, Germany (for a few months)
1986 AT&T Bell Labs, New Jersey (2 months) Imperial College, London (3 months) Dortmund, Germany
1990 Novosibirsk, USSR (by invitation) (2 weeks) Vienna, Scientific Computation Conference (in honour of H. J. Stetter) Helsinki conference on Numerical Methods for Ordinary Differential Equations
1991 University of Manchester, England (3 months) Universiteit te Leiden, Holland. Kloostermann Professor (2 months) Arizona State University, Phoenix, Arizona (3 months)
1992 Co-organiser of: "International Conference on Scientific Computation and Differential Equations", Auckland 4-8 January 1993 (in honour of J. C. Butcher's 60th birthday) University Of Durham - Workshop on numerical methods for evolutionary problems
1993 August, September - Brazil (Rio de Janeiro; Uberlandia) November, December - USA (Lafayette; Phoenix, Arizona; Raleigh, Nth Carolina)
1994 July - New Orleans; Atlanta, Georgia August, September - Phoenix, Arizona; Miskolc, Hungary; Rennes, Marseilles, France
1995 January - Phoenix, Arizona; Stockholm, Sweden; London, England March - Stanford, California (Gear conference) June - Geiranger, Norway; Dundee, Scotland August, September - Sao Jose do Rio Preto and Curitiba, Brazil Porto and Coimbra, Portugal; Valladolid and Zaragoza, Spain September to December - Rennes, France; Amsterdam, Netherlands; Cambridge, England
1996 January, February, March - Troy, New York April, May - Brisbane, Australia May, June - Phoenix, Arizona; Toronto, Canada
1997 August, September - Berlin, Germany; Alexisbad, Germany; Grado, Italy
Publications
See John Butcher's publications</A)<>
Please find more details from
http://www.math.auckland.ac.nz/~butcher/
|
Recent publications
| | 1. Construction of high order diagonally implicit multistage integration methods for ordinary differential equations, with Z. Jackiewicz, Appl. Numer. Math. 27 (1998), 1-12.
2.
Efficient Runge-Kutta integrators for index-$2$ differential algebraic equations, with R. P. K. Chan, Math. Comp. 67 (1998), 1001-1021.
3.
DESIRE: diagonally extended singly implicit Runge-Kutta effective order methods, with M.T. Diamantakis, Numer. Algorthms, 17 (1998), 121-145.
4. ARK methods up to order five, Numer. Algorithms, 17 (1998), 193-221.
5. Order and effective order, Appl. Numer. Math., 28 (1998), 179-191.
6. ESIRK methods and variable stepsize, with D. J. L. Chen, Appl. Numer.
Math., 28 (1998), 193-207.
7. The effective order of singly-implicit Runge-Kutta methods, with P. Chartier, Numer. Algorithms, 20 (1999), 269-284.
8. An area theorem for the same-different experiment, with R.J. Irwin and M.J. Hautus, Perception & Psychophysics, 61(4) (1999), 766-769.
9. Experiments with a
variable-order type 1 DIMSIM code, with P. Chartier and Z. Jackiewicz, Numerical Algorithms, 22 (1999), 237-261.
10. The choice of parameters in parallel general linear methods for stiff problems, with A.D. Singh, Appl. Numer. Math., 34(1) (2000), 59-84.
11. Multi-step zero approximations for stepsize control, with T.M.H. Chan, Appl. Numer. Math., 34 (2000), 167-177.
12. A new type of singly-implicit Runge-Kutta method, with D.J.L. Chen, Appl. Numer. Math., 34 (2000), 179-188.
13. Numerical methods for ordinary differential equations in the 20th century, J. Comput. Appl. Math., 125 (2000), 1-29.
14. General linear methods for stiff differential equations, BIT, 41 (2001), 240-264.
15. Variable stepsize schemes for effective order methods and enhanced order composition methods, with T. M. H. Chan, Numer. Algorithms, 26 (2001), 131-150.
16. On the implementation of ESIRK methods for stiff IVPs, with D. J. L. Chen, Numer. Algorithms, 26 (2001), 201-218.
Please find more details from
http://www.math.auckland.ac.nz/~butcher/
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