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Mathematics - Computational Science & Engineering | The Concept of Stability in Numerical Mathematics

The Concept of Stability in Numerical Mathematics

Hackbusch, Wolfgang

2014, XV, 188 p.

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  • Offers a self-contained presentation of aspects of stability in numerical mathematics
  • Compares and characterizes stability in different subfields of numerical mathematics
  • Covers numerical treatment of ordinary differential equations, discretisation of partial differential equations, discretisation of integral equations and more

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.

 

Content Level » Research

Keywords » differential equations - integral equations - interpolation - quadature - stability

Related subjects » Analysis - Computational Science & Engineering - Dynamical Systems & Differential Equations

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