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Asymptotic solvers for second-order differential equation systems with multiple frequencies

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Abstract

In this paper, an asymptotic expansion is constructed to solve second-order differential equation systems with highly oscillatory forcing terms involving multiple frequencies. An asymptotic expansion is derived in inverse of powers of the oscillatory parameter and its truncation results in a very effective method of dicretizing the differential equation system in question. Numerical experiments illustrate the effectiveness of the asymptotic method in contrast to the standard Runge–Kutta method.

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Correspondence to Jing Gao.

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The work was supported by the Natural Science Foundation of China (NSFC) (Grant No. 11201370, 11171270) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090201120061) and the Fundamental Research Funds for the Central Universities.

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Condon, M., Deaño, A., Gao, J. et al. Asymptotic solvers for second-order differential equation systems with multiple frequencies. Calcolo 51, 109–139 (2014). https://doi.org/10.1007/s10092-013-0078-4

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  • DOI: https://doi.org/10.1007/s10092-013-0078-4

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