The Graduate Student's Guide To Numerical Analysis '98: Lecture Notes From The Viii Epsrc Summer School In Numerical Analysis (springer Series In Computational Mathematics)

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own. Recent graduates in mathematical sciences who are considering the possibility of a pursuing research towards a PhD in applied mathematics or numerical analysis should also find this book a very valuable guide. The Eighth EPSRC Numerical Analysis Summer School was held at the Uni­ versity of Leicester from the 5th to the 17th of July, 1998. This was the third Numerical Analysis Summer School to be held in Leicester. The previous meetings, in 1992 and 1994, had been carefully structured to ensure that each week had a coherent 'theme'. For the 1998 meeting, in order to widen the audience, we decided to relax this constraint. Speakers were chosen to cover what may appear, at first sight, to be quite diverse areas of numeri­ cal analysis. However, we were pleased with the extent to which the ideas cohered, and particularly enjoyed the discussions which arose from differing interpretations of those ideas. We would like to thank all six of our main speakers for the care which they took in the preparation and delivery of their lectures. In this volume we present their lecture notes in alphabetical rather than chronological order. Nick Higham, Alastair Spence and Nick Trefethen were the speakers in week 1, while Bernardo Cockburn, Stig Larsson and Bob Skeel were the speakers in week 2. Another new feature of this meeting compared to its predecessors was that we had 'invited seminars'. A numer of established academics based in the UK were asked to participate in the afternoon seminar program. Front Matter....Pages I-XI A Simple Introduction to Error Estimation for Nonlinear Hyperbolic Conservation Laws....Pages 1-45 Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra....Pages 47-82 Numerical Analysis of Semilinear Parabolic Problems....Pages 83-117 Integration Schemes for Molecular Dynamics and Related Applications....Pages 119-176 Numerical Methods for Bifurcation Problems....Pages 177-216 Spectra and Pseudospectra....Pages 217-250 Back Matter....Pages 251-252 B. Cockburn: A Simple Introduction to Error Estimation for Nonlinear Hyperbolic Conservation Laws N.J. Higham: Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra S. Larsson: Numerical Analysis of Semilinear Parabolic Problems R.D. Skeel: Integration schemes for molecular dynamics and related applications A. Spence and I.G. Graham: Numerical Methods for Bifurcation Problems L.N. Trefethen: Spectra and Pseudospectra. Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography.