Theory and Numerics of Differential Equations

1. Front Matter

   Pages I-X

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2. Spectral, Spectral Element and Mortar Element Methods

   • Christine Bernardi, Yvon Maday

   Pages 1-57

3. Numerical Analysis of Microstructure

   • Carsten Carstensen

   Pages 59-126

4. Maple for Stochastic Differential Equations

   • S. Cyganowski, L. Grüne, P. E. Kloeden

   Pages 127-177

5. Nonlinear Multigrid Techniques

   • Ralf Kornhuber

   Pages 179-229

6. Hyperbolic Differential Equations and Adaptive Numerics

   • Kyoung-Sook Moon, Anders Szepessy, Raúl Tempone, Georgios Zouraris

   Pages 231-280

7. Back Matter

   Pages 281-282

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The Ninth EPSRC Numerical Analysis Summer School was held at the Uni­ versity of Durharn, UK, from the 10th to the 21st of July 2000. This was the first of these schools to be held in Durharn, having previously been hosted, initially by the University of Lancaster and latterly by the University of Leicester. The purpose of the summer school was to present high quality in­ structional courses on topics at the forefront of numerical analysis research to postgraduate students. Eminent figures in numerical analysis presented lectures and provided high quality lecture notes. At the time of writing it is now more than two years since we first con­ tacted the guest speakers and during that period they have given significant portions of their time to making the summer school, and this volume, a suc­ cess. We would like to thank all six of them for the care which they took in the preparation and delivery of their lectures. The speakers were Christine Bernardi, Petter Bj0rstad, Carsten Carstensen, Peter Kloeden, Ralf Kornhu­ ber and Anders Szepessy. This volume presents written contributions from five of the six speakers. In all cases except one, these contributions are more comprehensive versions of the lecture not es which were distributed to participants during the meeting. Peter Kloeden's contribution is intended to be complementary to his lecture course and numerous references are given therein to sources of the lecture material.

• calculus
• differential equation
• microstructrue
• multigrid
• numerical analysis
• numerics
• partial differential equation
• spectral and high order methods
• stochastic and hyperbolic partial differential equations

From the reviews of the first edition:

"This book contains detailed lecture notes on five 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. Current (unsolved) problems are also described and directions for future research are given. The book is suitable for first year graduate students in applied mathematics and for professional mathematicians." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

• Department of Mathematical Sciences Science Laboratories, University of Durham, Durham, UK

  James F. Blowey, John P. Coleman, Alan W. Craig

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