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.