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Historical Developments in Singular Perturbations pp 53–121Cite as

The Method of Matched Asymptotic Expansions and Its Generalizations

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Abstract

Milton Van Dyke’s Perturbation Methods in Fluid Mechanics [490] was effectively both the earliest and the most influential book specifically about applied singular perturbations. (Some credit might be given earlier fluid dynamics textbooks, e.g., Hayes and Probstein [199]). Van Dyke extensively surveyed the large extant aeronautical and fluid dynamical literature, forcefully advocating and clarifying the so-called method of matched asymptotic (or inner and outer) expansions . Although Van Dyke acknowledged that Prandtl’s boundary layer theory was the prototype singular perturbation problem, he introduced the subject by describing incompressible fluid flow past a thin airfoil. The book’s highlight message, sometimes called Van Dyke’s magic rule , states:

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  1. Department of Applied Mathematics, University of Washington, Seattle, WA, USA

    Robert E. O’Malley

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O’Malley, R.E. (2014). The Method of Matched Asymptotic Expansions and Its Generalizations. In: Historical Developments in Singular Perturbations. Springer, Cham. https://doi.org/10.1007/978-3-319-11924-3_3

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