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.
• The first book devoted to high oscillation, covering the full breadth of the subject area • Authored by leading experts in their respective fields • Surveys the current state of the field and paves the way for future research
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.