Theory and Numerics of Differential Equations

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, and graduates in mathematical sciences.

Inhalt

Spectral, Spectral Element and Mortar Element Methods.- Numerical Analysis of Microstructure.- Maple for Stochastic Differential Equations.- Nonlinear Multigrid Techniques.- Hyperbolic Differential Equations and Adaptive Numerics.