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The Concept of Stability in Numerical Mathematics de Wolfgang Hackbusch

The Concept of Stability in Numerical Mathematics: Springer Series in Computational Mathematics, cartea 45

Autor Wolfgang Hackbusch
en Limba Engleză Hardback – 20 feb 2014
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.
 
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Specificații

ISBN-13: 9783642393853
ISBN-10: 3642393853
Pagini: 200
Ilustrații: XV, 188 p.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.47 kg
Ediția:2014
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Springer Series in Computational Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Recenzii

“The contents are presented in a way that isaccessible to graduate students who may use the book for self-study of thetopic, and it can easily be used as a textbook for a corresponding lectureseries. Moreover, advanced researchers in numerical mathematics are likely tobenefit from reading it, in particular because the book provides interestinginsight into how stability relates to areas other than their own particularspecialization field. … also useful reading material for numerical softwaredevelopers.” (Kai Diethelm, Computing Reviews, October, 2015)
“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)

Notă biografică

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".

Textul de pe ultima copertă

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.
 

Caracteristici

Offers a self-contained presentation of aspects of stability in numerical mathematics Compares and characterizes stability in different subfields of numerical mathematics Covers numerical treatment of ordinary differential equations, discretisation of partial differential equations, discretisation of integral equations and more Includes supplementary material: sn.pub/extras