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The Concept of Stability in Numerical Mathematics
Wolfgang Hackbusch
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Description for The Concept of Stability in Numerical Mathematics
Paperback. This book offers a self-contained presentation of aspects of stability in numerical mathematics. It compares and characterizes stability in different subfields of numerical mathematics. Series: Springer Series in Computational Mathematics. Num Pages: 203 pages, biography. BIC Classification: PBKJ; PBKL; PBKS. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 11. Weight in Grams: 320.
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 ... Read moresubfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
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Product Details
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Series
Springer Series in Computational Mathematics
Place of Publication
Berlin, Germany
Shipping Time
Usually ships in 15 to 20 working days
About Wolfgang Hackbusch
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 ... Read moreof hierarchical matrices. Hackbusch is also in the editorial board of Springer's book series "Advances in Numerical Mathematics" and "The International Cryogenics Monograph Series". Show Less
Reviews for The Concept of Stability in Numerical Mathematics
“The contents are presented in a way that is accessible to graduate students who may use the book for self-study of the topic, and it can easily be used as a textbook for a corresponding lecture series. Moreover, advanced researchers in numerical mathematics are likely to benefit from reading it, in particular because the book provides interesting insight into how ... Read morestability relates to areas other than their own particular specialization field. … also useful reading material for numerical software developers.” (Kai Diethelm, Computing Reviews, October, 2015) “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 für Angewandte Mathematik und Mechanik, Vol. 94 (9), 2014) Show Less