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arXiv · 1506.06308

Asymptotic solvers for ordinary differential equations with multiple frequencies

Marissa Condon·Alfredo Deano·Jing Gao·Arieh Iserles
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Abstract

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method.

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Marissa Condon, Alfredo Deano, Jing Gao, Arieh Iserles. 2015-06-21. Asymptotic solvers for ordinary differential equations with multiple frequencies. https://doi.org/10.1007/s11425-015-5066-5

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