ENGLISH

The Concept of Stability in Numerical Mathematics

By Wolfgang Hackbusch (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2014
ISBN
978-3-642-39385-3, 978-3-642-39386-0
DOI
10.1007/978-3-642-39386-0
Language
english
Format
PDF
Filesize
2 MB (2457320 bytes)
Series
Springer Series in Computational Mathematics 45
Edition
1
Pages
188\202
Time added
2014-04-13 05:00:00
Numerical Analysis; Partial Differential Equations

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.

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