The Concept of Stability in Numerical Mathematics.pdf

The Concept of Stability in Numerical Mathematics

Wolfgang Hackbusch

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. 

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 The Concept of Stability in Numerical Mathematics Springer ...

4.61 MB DATEIGRÖSSE
3642393853 ISBN
Englisch SPRACHE
The Concept of Stability in Numerical Mathematics.pdf

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W. Hackbusch: The Concept of Stability in Numerical Mathematics, Springer Series in Computational Mathematics, Vol. 45, Springer 2014 The Concept of Stability in Numerical …

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The main computational costs of these two methods are connected with solving systems ... Our attempts to use the block structure typical for hydrodynamic stability ... at kth iteration of Algorithm 2, where the preconditioner matrix Pk defined in ...

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Springer Series in Computational Mathematics: 45 The ...