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This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "reallife" problems in applied mathematics, in particular problems that do not have a closedform solution. Contributions on both initialvalue problems and boundaryvalue problems in ordinary differential equations appear in this volume. Numerical methods for initialvalue problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (onestep methods) and those which are based on several values of the solution (multistep methods). John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initialvalue problems using RungeKutta and Rosenbrock methods, with interpolants to fill in the solution between meshpoints, but the 'slant' is new  based on the question, "How should such software integrate into the current generation of Problem Solving Environments?" Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices. The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour. Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. Arieh Iserles and Antonella Zanna survey the construction of RungeKutta methods which preserve algebraic invariant functions. Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of HÃ©non and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions. Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on Astable multistep methods and Butcher's first paper on implicit RungeKutta methods. Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory. Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted RungeKutta methods with s stages. Differentialalgebraic equations arise in control, in modelling of mechanical systems and in many other fields. Jeff Cash describes a fairly recent class of formulae for the numerical solution of initialvalue problems for stiff and differentialalgebraic systems. Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initialvalue problems. Again in the area of differentialalgebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE twopoint boundaryvalue problems. Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect To view this DRM protected ebook on your desktop or laptop you will need to have Adobe Digital Editions installed. It is a free software. We also strongly recommend that you sign up for an AdobeID at the Adobe website. For more details please see FAQ 1&2. To view this ebook on an iPhone, iPad or Android mobile device you will need the Adobe Digital Editions app, or BlueFire Reader or Txtr app. These are free, too. For more details see this article.
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Ebook Details 

Pages:  558 
Size:  75.6 MB 
Publisher:  North Holland 
Date published:  2001 
ISBN:  9780080929552 (DRMPDF)

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Copying:  allowed  Printing:  allowed  Read Aloud:  not allowed 
