Titlebook: Solving Ordinary Differential Equations II; Stiff and Differenti Ernst Hairer,Gerhard Wanner Book 1996Latest edition Springer-Verlag Berlin

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B-Stability and ContractivityHere we enter a new era, the study of stability and convergence for general . systems. All the “crimes” and diverse omissions of which we have been guilty in earlier sections, especially in Sect. IV.2, shall now be repaired.

Mechanics

Positive Quadrature Formulas and B-Stable RK-MethodsWe shall give a constructive characterization of all irreducible . -stable Runge-Kutta methods (Theorem 13.15). Because of Theorem 12.16 we first have to study quadrature formulas with positive weights.

Finasteride

B-ConvergenceProthero & Robinson (1974) were the first to discover the order reduction of implicit Runge-Kutta methods when applied to stiff differential equations. Frank, Schneid & Ueberhuber (1981) then introduced the “concept of . -convergence”, which furnishes global error estimates independent of the stiffness.

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Stability of Multistep MethodsA general .-step multistep method is of the form

incubus

concubine

时代

978-3-642-05220-0Springer-Verlag Berlin Heidelberg 1996

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Solving Ordinary Differential Equations II978-3-642-05221-7Series ISSN 0179-3632 Series E-ISSN 2198-3712

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Stress-Fracture