A method for incorporating transcendentally small terms into the method of matched asymptotic expansions

被引:12
作者
MacGillivray, AD
机构
[1] Department of Mathematics, State University of New York, Buffalo
[2] State University of New York, Buffalo, NY
关键词
D O I
10.1111/1467-9590.00062
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The essential ideas behind st method for incorporating exponentially small terms into the method of matched asymptotic expansions are demonstrated using an Ackerberg-O'Malley resonance problem and a spurious solutions problem of Carrier and Pearson. One begins with the application of the standard method of matched asymptotic expansions to obtain at least the leading terms in outer and inner (Poincare-type) expansions; some, although not all, matching can be carried out at this stage. This is followed by the introduction of supplementary expansions whose gauge functions are transcendentally small compared to those in the standard expansions. Analysis of terms in these expansions allows the matching to be completed. Furthermore, the method allows for the inclusion of globally valid transcendentally small contributions to the asymptotic solution; it is well known that such terms may be numerically significant.
引用
收藏
页码:285 / 310
页数:26
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