The Concept of Stability in Numerical Mathematics [Paperback]

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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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.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.

The contents are presented in a way that isaccessible to graduate students who may use the book for self-study of thetopic, and it can easily be used as a textbook for a corresponding lectureseries. Moreover, advanced researchers in numerical mathematics are likely tobenefit from reading it, in particular because the book provides interestinginsight into how stability relates to areas other than their own particularspecialization field. & also useful reading material for numerical softwaredevelopers. (Kai Diethelm, Computing Reviews, October, 2015)

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