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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