Author	Hackbusch, Wolfgang. author
Title	The Concept of Stability in Numerical Mathematics [electronic resource] / by Wolfgang Hackbusch
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014
Connect to	http://dx.doi.org/10.1007/978-3-642-39386-0
Descript	XV, 188 p. online resource

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.  

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

1. Mathematics
2. Integral equations
3. Partial differential equations
4. Numerical analysis
5. Mathematics
6. Numerical Analysis
7. Partial Differential Equations
8. Integral Equations