The Concept of Stability in Numerical Mathematics (Springer Series in Computational Mathematics Book 45)

Annotation 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 Front Matter....Pages i-xv Introduction....Pages 1-2 Stability of Finite Algorithms....Pages 3-15 Quadrature....Pages 17-45 Interpolation....Pages 47-62 Ordinary Differential Equations....Pages 63-92 Instationary Partial Differential Equations....Pages 93-138 Stability for Discretisations of Elliptic Problems....Pages 139-166 Stability for Discretisations of Integral Equations....Pages 167-184 Back Matter....Pages 185-188