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Asymptotic least squares approximation for highly oscillatory differential equations

Olver, S (Cambridge)
Thursday 05 July 2007, 11:00-11:30

Seminar Room 1, Newton Institute


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.



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