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The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods
Rok: 1987
ISBN: 9780471910466
OKCZID: 110389591
Citace (dle ČSN ISO 690):
BUTCHER, J. C. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Chichester: J. Wiley, c1987. 15, 512 s.
Anotace
This book introduces the subject of numerical methods for ordinary differential equations and deals in detail with Runge- Kutta and general linear methods. Although present differential equation software is dominated by implementations of linear multistep methods, so that Runge- Kutta methods are less widely used in practice, it is the author's claim that their potential efficacy has not yet been fully realised. By presenting a detailed analysis of these methods and of the less familiar class of general linear methods, it is hoped to foster further interest in their implementation. It contains an analysis of the order conditions for Runge- Kutta methods using a combinatorial approach and shows how the analysis extends to general linear methods. It also deals with recent work on such topics as nonlinear stability for differential equations algorithms and looks in detail at practical questions related to efficient implementation. A substantial bibliography, fully comprehensive up to 1982, is included.