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

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Extrapolation Methodsthe idea of extrapolation can also be used for stiff problems. We shall use the results of Sect. I1.8 for the existence of asymptotic expansions and apply them to the study of those implicit and linearly implicit methods, which seem to be most suitable for the computation of stiff differential equat

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Contractivity for Linear Problems6) of Sect. IV.2). Especially for large-dimensional problems, however, the matrix which performs this transformation may be badly conditioned and destroy all the nice estimations which have been obtained.

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Book 1996Latest edition years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth­ ods

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Springer Series in Computational Mathematicshttp://image.papertrans.cn/s/image/871797.jpg

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https://doi.org/10.1007/978-3-642-05221-7Differential-algebraic systems; Differentialgeichung; Numerical analysis; Numerik; Ordinary differential

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Examples of Stiff EquationsStiff equations are problems for which explicit methods don’t work. Curtiss & Hirschfelder (1952) explain stiffness on one-dimensional examples such as

Pde5-Inhibitors

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Implementation of Implicit Runge-Kutta MethodsIf the dimension of the differential equation . = .(.) is ., then the . -stage fully implicit Runge-Kutta method (3.1) involves a . -dimensional nonlinear system for the unknowns .., ... , ... An efficient solution of this system is the main problem in the implementation of an implicit Runge-Kutta method.

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Numerical ExperimentsAfter having seen so many different methods and ideas in the foregoing sections, it is legitimate to study how all these theoretical properties pay off in numerical efficiency.