The Concept of Stability in Numerical Mathematics / Springer Series in Computational Mathematics Bd.45 (PDF)
Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of...
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In this book, the author compares the meaning of stability in different subfields of numerical mathematics.
Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.
In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
- Autor: Wolfgang Hackbusch
- 2014, 2014, 188 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3642393861
- ISBN-13: 9783642393860
- Erscheinungsdatum: 06.02.2014
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Grösse: 2.34 MB
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“This book is concerned with stability properties invarious areas of numerical mathematics, and their strong connection withconvergence of numerical algorithms. As a side effect, any parts of numericalanalysis are reviewed in the course of the stability discussions. The book aimsin particular at master and Ph.D. students.” (M. Plum, zbMATH 1321.65139, 2015)
“This nontraditional book by Hackbusch (Max Planck Institute for Mathematics in the Sciences, Germany) headlines the abstract stability concept. … ultimately serves a broad but unusually thoughtful introduction to (or reexamination of) numerical analysis. Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (4), December, 2014)
“It is the perfect complement to a lecture series on numerical analysis, starting with stability of finite arithmetic, quadrature and interpolation, followed by ODE, time-dependent PDE, Elliptic PDE, and integral equations. … All chapters are presented self-contained with separate reference list, so that they can be studied independently. … it is highly recommended for all lectures and all students in applied and numerical mathematics.” (Christian Wieners, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 94 (9), 2014)
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