Algebraic Analysis of Singular Perturbation Theory
Algebraic Analysis of Singular Perturbation Theory
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DOI：
10.1090/mmono/227
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
T. Kawai;Yoshitsugu Takei
中科院分区：
文献类型：
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作者：
T. Kawai;Yoshitsugu Takei
本书的主题是研究常微分方程的奇异扰动，即将解表示为渐近级数而不是扰动参数中的解析函数的扰动。使用的主要方法是所谓的 WKB（Wentzel-Kramers-Brillouin）方法，最初是为研究量子力学系统而发明的。作者详细描述了 WKB 方法及其在 Fuchsian 微分方程单调问题研究和 Painleve 函数分析中的应用。本书适合对微分方程和特殊函数感兴趣的研究生和研究人员。
The topic of this book is the study of singular perturbations of ordinary differential equations, ie, perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.