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**Singular perturbation methods for ordinary differential equations.**
*(English)*
Zbl 0743.34059

Applied Mathematical Sciences. 89. New York etc.: Springer-Verlag. viii, 225 p. (1991).

This book is a continuation of a former one of the author [Introduction to Singular Perturbations, Acad. Press, New York (1974; Zbl 0287.34062)]. It deals with singularly perturbed initial and boundary value problems, respectively, both for linear and nonlinear systems of ordinary differential equations. As usual, first there are constructed inner and outer solutions, afterwards they are matched at the edge of Prandtl’s boundary layer. Turning point problems are treated as well. Further topics are stability considerations, the localization of shock layers, the numerical solution of stiff differential equations, and so called singular perturbations. The last term concerns the critical case that the reduced problem has infinitely many solutions. No theorems are formulated explicitly, but every section contains striking examples or applications to different domains as control theory, gas and fluid dynamics, oscillations and semi-conductor problems. The well written book contains 64 illustrations, many exercises and 16 pages of references. It ends with a survey about the history of singular perturbations.

Reviewer: L.Berg

### MSC:

34E15 | Singular perturbations for ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

34E20 | Singular perturbations, turning point theory, WKB methods for ordinary differential equations |

34-02 | Research exposition (monographs, survey articles) pertaining to ordinary differential equations |

34C25 | Periodic solutions to ordinary differential equations |