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The Method of Matched Asymptotic Expansions and Its Generalizations

In: Historical Developments in Singular Perturbations

Author

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  • Robert E. O’Malley

    (University of Washington, Department of Applied Mathematics)

Abstract

Milton Van Dyke’s Van Dyke, M. Perturbation Methods in Fluid Mechanics [490] Perturbation Methods in Fluid Mechanics 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 matched asymptotic expansions outer expansion . 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 Van Dyke, M. magic rule , states:

Suggested Citation

  • Robert E. O’Malley, 2014. "The Method of Matched Asymptotic Expansions and Its Generalizations," Springer Books, in: Historical Developments in Singular Perturbations, edition 127, chapter 0, pages 53-121, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-11924-3_3
    DOI: 10.1007/978-3-319-11924-3_3
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