Hadamard Expansions and Hyperasymptotic Evaluation
An Extension of the Method of Steepest Descents
Seiten
2011
Cambridge University Press (Verlag)
978-1-107-00258-6 (ISBN)
Cambridge University Press (Verlag)
978-1-107-00258-6 (ISBN)
For applied mathematicians and physical scientists interested in asymptotic calculations, this book describes a brand new method for the high-precision evaluation of Laplace integrals. Developed over the past decade, this method builds on the classical asymptotic method of steepest descents. Many numerical examples are included to illustrate the accuracy achievable.
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
R. B. Paris is a Reader in Mathematics in the Division of Complex Systems at the University of Abertay, Dundee.
Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications; Appendix A; Appendix B; Appendix C; References; Index.
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 30 Tables, black and white; 70 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 160 x 240 mm |
| Gewicht | 530 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-107-00258-3 / 1107002583 |
| ISBN-13 | 978-1-107-00258-6 / 9781107002586 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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