Highly Oscillatory Problems

The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sciences, which was the first time that different specialists in highly oscillatory research, from diverse areas of mathematics and applications, had been brought together for a single intellectual agenda. This ground-breaking volume consists of eight review papers by leading experts in subject areas of active research, with an emphasis on computation: numerical Hamiltonian problems, highly oscillatory quadrature, rapid approximation of functions, high frequency wave propagation, numerical homogenization, discretization of the wave equation, high frequency scattering and the solution of elliptic boundary value problems.

Preface; 1. Oscillations over long times in numerical Hamiltonian systems E. Hairer and C. Lubich; 2. Highly oscillatory quadrature D. Huybrechs and S. Olver; 3. Rapid function approximation by modified Fourier series D. Huybrechs and S. Olver; 4. Approximation of high frequency wave propagation M. Motamed and O. Runborg; 5. Wavelet-based numerical homogenization B. Engquist and O. Runborg; 6. Plane wave methods for approximating the time harmonic wave equation T. Luostari, T. Huttunen and P. Monk; 7. Boundary integral methods in high frequency scattering S. N. Chandler-Wilde and I. G. Graham; 8. Novel analytical and numerical methods for elliptic boundary value problems A. S. Fokas and E. A. Spence.

This ground-breaking volume assembles experts in different areas of active research into highly oscillatory problems, with a particular emphasis on computation. The publication of these articles came about after the huge wave of interest that followed the very successful six-month programme held at the Newton Institute of Mathematical Sciences.

Bjorn Engquist currently holds the Computational and Applied Mathematics Chair I at the University of Texas at Austin, as well as a chair in numerical analysis at the Royal Institute of Technology in Stockholm. He is a member of the Royal Swedish Academy of Sciences and the Royal Swedish Academy of Engineering Sciences.
Athanasios Fokas is Professor of Nonlinear Mathematical Science at the University of Cambridge. He is a member of the Academy of Athens, and a recipient of the London Mathematical Society Naylor Prize and the Aristeon Prize in Sciences.
Ernst Hairer is a Professor of Mathematics at the University of Geneva and has been awarded the Henrici Prize by the Society of Industrial and Applied Mathematics.
Arieh Iserles holds the chair of Numerical Analysis of Differential Equations at the University of Cambridge and was awarded the Onsager Medal of the Norwegian University of Science and Technology.