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Engels  9780444506009  558 pagina's
C. t. H. Baker, G. Vanden Berghe  9780444506009
Engels  9780444506009  558 pagina's
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 Henon 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 attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and attempting to estimate the defect  the amount by which the approximation fails to satisfy the given equation and any sideconditions. The paper by Wayne Enright on defect control relates to carefully analyzed techniques that have been proposed both for ordinary differential equations and for delay differential equations in which an attempt is made to control an estimate of the size of the defect. Many phenomena incorporate noise, and the numerical solution of stochastic differential equations has developed as a relatively new item of study in the area. Keven Burrage, Pamela Burrage and Taketomo Mitsui review the way numerical methods for solving stochastic differential equations (SDE's) are constructed. One of the more recent areas to attract scrutiny has been the area of differential equations with aftereffect (retarded, delay, or neutral delay differential equations) and in this volume we include a number of papers on evolutionary problems in this area. The paper of Genna Bocharov and Fathalla Rihan conveys the importance in mathematical biology of models using retarded differential equations. The contribution by Christopher Baker is intended to convey much of the background necessary for the application of numerical methods and includes some original results on stability and on the solution of approximating equations. Alfredo Bellen, Nicola Guglielmi and Marino Zennaro contribute to the analysis of stability of numerical solutions of nonlinear neutral differential equations. Koen Engelborghs, Tatyana Luzyanina, Dirk Roose, Neville Ford and Volker Wulf consider the numerics of bifurcation in delay differential equations. Evelyn Buckwar contributes a paper indicating the construction and analysis of a numerical strategy for stochastic delay differential equations (SDDEs). This volume contains contributions on both Volterra and Fredholmtype integral equations. Christopher Baker responded to a late challenge to craft a review of the theory of the basic numerics of Volterra integral and integrodifferential equations. Simon Shaw and John Whiteman discuss Galerkin methods for a type of Volterra integral equation that arises in modelling viscoelasticity. A subclass of boundaryvalue problems for ordinary differential equation comprises eigenvalue problems such as SturmLiouville problems (SLP) and Schrodinger equations. Liviu Ixaru describes the advances made over the last three decades in the field of piecewise perturbation methods for the numerical solution of SturmLiouville problems in general and systems of Schrodinger equations in particular. Alan Andrew surveys the asymptotic correction method for regular SturmLiouville problems. Leon Greenberg and Marco Marletta survey methods for higherorder SturmLiouville problems. R. Moore in the 1960s first showed the feasibility of validated solutions of differential equations, that is, of computing guaranteed enclosures of solutions. Boundary integral equations. Numerical solution of integral equations associated with boundaryvalue problems has experienced continuing interest. Peter Junghanns and Bernd Silbermann present a selection of modern results concerning the numerical analysis of onedimensional Cauchy singular integral equations, in particular the stability of operator sequences associated with different projection methods. Johannes Elschner and Ivan Graham summarize the most important results achieved in the last years about the numerical solution of onedimensional integral equations of Mellin type of means of projection methods and, in particular, by collocation methods. A survey of results on quadrature methods for solving boundary integral equations is presented by Andreas Rathsfeld. Wolfgang Hackbusch and Boris Khoromski present a novel approach for a very efficient treatment of integral operators. Ernst Stephan examines multilevel methods for the h, p and hp versions of the boundary element method, including preconditioning techniques. George Hsiao, Olaf Steinbach and Wolfgang Wendland analyze various boundary element methods employed in local discretization schemes.
Levertijd:

Ordinary Differential Equations and Integral Equations Engels  9780444506009  558 pagina's  

Taal  Engels 
Verschijningsdatum  juni 2001 
Aantal pagina's  558 pagina's 
Illustraties  Met illustraties 
Auteur  C. t. H. Baker  G. Vanden Berghe 
Coauteur  G. Vanden Berghe 
Redacteur  J. D. Pryce 
Uitgever  Elsevier Science & Technology 
Originele Titel  Ordinary Differential Equations and Integral Equations 
Bindwijze  Paperback 
Editie  6 
Extra groot lettertype  Nee 
Subtitel  Volume 6 
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