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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

Asymptotic least squares approximation for highly oscillatory differential equations

Author: Sheehan Olver (Cambridge)

Abstract

This talk presents a new approach for approximating highly oscillatory ordinary differential equations. By using the asymptotic expansion in a least squares system, we are able to obtain a result that preserves the asymptotic accuracy of the expansion, while converging rapidly to the exact solution. We are thus able to accurately approximate such differential equations by solving a very small linear system. We apply this method to the computation of highly oscillatory integrals, as well as second order oscillatory differential equations.