The Concept of Stability in Numerical Mathematics

By:

Wolfgang Hackbusch

Format:

Paperback / softback

Series:

Springer Series in Computational Mathematics

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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.

Author Biography:

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".

Release date Australia

August 23rd, 2016

Author

Wolfgang Hackbusch

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2014

Illustrations

XV, 188 p.

Pages

188

Series

Springer Series in Computational Mathematics

Dimensions

155x235x11

ISBN-13

9783662513712

Product ID

25697068

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