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Numerical Analysis:
A R Mitchell 75th Birthday Volume


D F Griffiths and G A Watson (Eds)

Pub. Date: June 1996. 380pp(approx), ISBN: 981-02-2719-1, World Scientific Publishing Company, Singapore



This Volume is intended as a small tribute to Ron Mitchell on the occasion of his 75th birthday, which falls on 22 June 1996. It consists of a collection of articles, written by people with links with Ron, as students, as colleagues, as co-workers, or just as regular visitors to Dundee. This set is of course very large, and we were obliged to restrict our requests for contributions to a subset, which was chosen in a somewhat arbitrary manner. Some of those who were not asked for contributions might feel disappointed or even offended: we very much regret if that is the case. Of course, some of those we did approach were, for various perfectly legitimate reasons, unable to provide us with a contribution within the given timescale. Since it will not be clear into which of these groups any particular person falls, we hope therefore that this venture will not lose us too many friends.

Some details of Ron's work and career are given elsewhere in this book but an explanation for its existence might be expected in a preface such as this. We could do this by drawing attention to the fact that Ron has made many substantial contributions to Numerical Analysis, both at a national and an international level, through his papers, his books, his conference talks, his visits, his supervision of students and of research fellows, his encouragement of young people, friends and colleagues. But that formal list does not do full justice to Ron. Because what is not included is the range of human qualities, the immense personal magnetism, the marvellous sense of humour. No attempt to characterise Ron would be complete without mention of these, because they are essential parts of a full picture. They are a major part of the reason why Ron is regarded in such high esteem, and with so much affection, by his friends and colleagues.

We are grateful to the World Scientific Publishing Company for giving us the opportunity to produce this book, and we would like to thank them, and in particular Dr Anju Goel for help in the pre-publication process. We have been privileged to have been members of the Numerical Analysis Group in Dundee, led by Ron, for over 25 years. We join with the other contributors to this volume in saying: ``Happy birthday, Ron, and many more of them''.

David F. Griffiths, G. Alistair Watson

Dundee, January, 1996



D. F. Griffiths, J. D. Lambert, G. A. Watson and G. Fairweather:
A. R. Mitchell: Some Biographical and Mathematical Notes Page: 1
Addendum: R. E. Barnhill: The Finite Element Method and Computer Aided Geometric Design Page: 9
Appendix 1: List of Publications of A. R. Mitchell Page: 11
Appendix 2: PhD Students of A. R. Mitchell Page: 19
M. Aves, P. J. Davies and D. J. Higham:
Fixed Points and Spurious Modes of a Nonlinear Infinite-Step Map Page: 21
J. C. Butcher:
Runge-Kutta Methods as Mathematical Objects Page: 39
M. Calvo, A. Iserles and A. Zanna:
Runge-Kutta Methods on Manifolds Page: 57
I. Christie, G. H. Ganser and J. W. Wilder:
Numerical Solutions of One and Two Dimensional Hyperbolic Systems Modelling a Fluidized Bed Page: 71
J. Douglas, Jr. and Daoqi Yang:
Numerical Experiments for a Nonoverlapping Domain Decomposition Method for Partial Differential Equations Page: 85
E. S. Fraga and J. Ll. Morris:
A Piecewise Uniform Adaptive Grid Algorithm for Nonlinear Dispersive Wave Equations Page: 99
G. H. Golub, D. J. Silvester and A. J. Wathen:
Diagonal Dominance and Positive Definiteness of Upwind Approximations for Advection Diffusion ProblemsPage: 125
B. M. Herbst, G. J. Le Roux and M. J. Ablowitz:
Chaos in Numerics Page: 133
D. P. Laurie and A. Craig:
Exact Difference Formulas for Linear Differential Operators Page: 155
M. A. Lopez-Marcos, J. M. Sanz-Serna and R. D. Skeel:
An Explicit Symplectic Integrator with Maximal Stability Interval Page: 163
V. S. Manoranjan:
A Two-Step Iterative Method Page: 177
K. W. Morton:
Coercivity for One-Dimensional Cell Vertex Approximations Page: 189
T. B. Nokonechny, P. Keast and P. H. Muir:
A Method of Lines Package, Based on Monomial Spline Collocation, for Systems of One Dimensional Parabolic Differential Equations Page: 207
M. R. Osborne:
Solving Least Squares Problems on Parallel Vector Processors Page: 225
M. R. Osborne and G. A. Watson:
Aspects of M-estimation and L_1 Fitting Problems Page: 247
G. M. Phillips:
On Generalized Bernstein Polynomials Page: 263
T. F. Russell and R. V. Trujillo:
The Finite Volume Element Method for Elliptic and Parabolic Equations Page: 271
S. W. Schoombie and E. Mare:
A Generalized Discrete Multiple Scales Analysis Technique Page: 291
D. M. Sloan and R. Wallace:
Numerical Solution of Burgers' Equation using a Two-Grid Method Page: 305
I. C. Smith, R. Wait and C. Addison:
The Effectiveness of Drop-Tolerance Based Incomplete Cholesky Preconditioners for the Conjugate Gradient Method Page: 325
G. Strang:
Creating and Comparing Wavelets Page: 345
Y. Tourigny:
The Numerical Analysis of Spontaneous Singularities in Nonlinear Evolution Equations Page: 355