The Concept of Stability in Numerical Mathematics
1st Edition
Published on 20. February 2014
Book
Hardback
XV, 188 pages
978-3-642-39385-3 (ISBN)
Description
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.
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.
Reviews / Votes
"This book is concerned with stability properties in various areas of numerical mathematics, and their strong connection with convergence of numerical algorithms. As a side effect, any parts of numerical analysis are reviewed in the course of the stability discussions. The book aims in 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 fur Angewandte Mathematik und Mechanik, Vol. 94 (9), 2014)More details
Product info
Book
Series
Language
English
Place of publication
Berlin, Heidelberg
Germany
Target group
Research
Illustrations
biography
Dimensions
Height: 244 mm
Width: 164 mm
Thickness: 17 mm
Weight
449 gr
ISBN-13
978-3-642-39385-3 (9783642393853)
DOI
10.1007/978-3-642-39386-0
Schweitzer Classification
Other editions
Additional editions
Wolfgang Hackbusch
The Concept of Stability in Numerical Mathematics
Book
08/2016
1st Edition
Springer
€53.49
Shipment within 7-9 days
Wolfgang Hackbusch
The Concept of Stability in Numerical Mathematics
E-Book
02/2014
1st Edition
Springer
€53.49
Available for download
Person
The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and a book in German about the technique of hierarchical matrices. Hackbusch is also in the editorial board of Springer's book series "Advances in Numerical Mathematics" and "The International Cryogenics Monograph Series".
Content
Preface.- Introduction.- Stability of Finite Algorithms.- Quadrature.- Interpolation.- Ordinary Differential Equations.- Instationary Partial Difference Equations.- Stability for Discretisations of Elliptic Problems.- Stability for Discretisations of Integral Equations.- Index.