Highly Oscillatory Problems

doi:10.1017/CBO9781139107136

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.

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Highly Oscillatory Problems

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-xiv

1 - Oscillations over long times in numerical Hamiltonian systems
pp 1-24

2 - Highly oscillatory quadrature
pp 25-50

3 - Rapid function approximation by modified Fourier series
pp 51-71

4 - Approximation of high frequency wave propagation problems
pp 72-97

5 - Wavelet-based numerical homogenization
pp 98-126

6 - Plane wave methods for approximating the time harmonic wave equation
pp 127-153

7 - Boundary integral methods in high frequency scattering
pp 154-193

8 - Novel analytical and numerical methods for elliptic boundary value problems
pp 194-239

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Highly Oscillatory Problems

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