{"product_id":"ordinary-differential-equations-and-integral-c-t-h-baker-9780444506009","title":"Ordinary Differential Equations and Integral Equations","description":"\u003cp\u003e\u003cbr\u003e\/homepage\/sac\/cam\/na2000\/index.html7-Volume Set now available at special set price !\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThis volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve real-life problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in \u003ci\u003eordinary differential equations\u003c\/i\u003e appear in this volume. Numerical methods for \u003ci\u003einitial-value problems\u003c\/i\u003e in ordinary differential equations fall naturally into two classes: those which use \u003ci\u003eone\u003c\/i\u003e starting value at each step (one-step methods) and those which are based on \u003ci\u003eseveral\u003c\/i\u003e values of the solution (multistep methods). \u003cbr\u003eJohn Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. \u003cbr\u003eRob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, How should such software integrate into the current generation of \u003ci\u003eProblem Solving Environments?\u003c\/i\u003e \u003cbr\u003eNatalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the \u003ci\u003en\u003c\/i\u003eth power of square matrices. \u003cbr\u003eThe dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of \u003ci\u003echaotic behaviour.\u003c\/i\u003e \u003cbr\u003eWilly Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. \u003cbr\u003eArieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions. \u003cbr\u003eValeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions. \u003cbr\u003e\u003ci\u003eStiff differential equations\u003c\/i\u003e first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on \u003ci\u003eA\u003c\/i\u003e-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods. \u003cbr\u003eErnst 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. \u003cbr\u003eGuido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with \u003ci\u003es\u003c\/i\u003e stages. \u003cbr\u003e\u003ci\u003eDifferential-algebraic equations\u003c\/i\u003e arise in control, in modelling of mechanical systems and in many other fields. \u003cbr\u003eJeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for \u003ci\u003estiff and differential-algebraic systems.\u003c\/i\u003e \u003cbr\u003eShengtai Li and Linda Petzold describe methods and software for \u003ci\u003esensitivity analysis\u003c\/i\u003e of solutions of DAE initial-value problems. \u003cbr\u003eAgain in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems. \u003cbr\u003eContrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual \u003ci\u003eerror\u003c\/i\u003e (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the \u003ci\u003edefect\u003c\/i\u003e - the amount by which the approximation fails to satisfy the given equation and any side-conditions. \u003cbr\u003eThe 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. \u003cbr\u003eMany phenomena incorporate noise, and the numerical solution of \u003ci\u003estochastic differential equations\u003c\/i\u003e has developed as a relatively new item of study in the area. \u003cbr\u003eKeven Burrage, Pamela Burrage and Taketomo Mitsui review the way numerical methods for solving stochastic differential equations (SDE's) are constructed. \u003cbr\u003eOne of the more recent areas to attract scrutiny has been the area of \u003ci\u003edifferential equations with after-effect\u003c\/i\u003e (retarded, delay, or neutral delay differential equations) and in this volume we include a number of papers on evolutionary problems in this area. \u003cbr\u003eThe paper of Genna Bocharov and Fathalla Rihan conveys the importance in mathematical biology of models using retarded differential equations. \u003cbr\u003eThe 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. \u003cbr\u003eAlfredo Bellen, Nicola Guglielmi and Marino Zennaro contribute to the analysis of stability of numerical solutions of nonlinear neutral differential equations. \u003cbr\u003eKoen Engelborghs, Tatyana Luzyanina, Dirk Roose, Neville Ford and Volker Wulf consider the numerics of bifurcation in delay differential equations. \u003cbr\u003eEvelyn Buckwar contributes a paper indicating the construction and analysis of a numerical strategy for stochastic delay differential equations (SDDEs). \u003cbr\u003eThis volume contains contributions on both \u003ci\u003eVolterra and Fredholm-type integral equations.\u003c\/i\u003e \u003cbr\u003eChristopher Baker responded to a late challenge to craft a review of the theory of the basic numerics of Volterra integral and integro-differential equations. \u003cbr\u003eSimon Shaw and John Whiteman discuss Galerkin methods for a type of Volterra integral equation that arises in modelling viscoelasticity. \u003cbr\u003eA subclass of \u003ci\u003eboundary-value problems\u003c\/i\u003e for ordinary differential equation comprises \u003ci\u003eeigenvalue problems\u003c\/i\u003e such as Sturm-Liouville\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e C. T. H. Baker,G. Monegato,G. Vanden Berghe\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0444506004\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780444506009\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Elsevier\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/20\/2001\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 558\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.74lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.25w x 1.14d\u003cbr\u003e\u003cbr\u003e\u003cb\u003eReview Citation(s): \u003c\/b\u003e\u003cbr\u003e\u003ci\u003eScitech Book News\u003c\/i\u003e 12\/01\/2001 pg. 43","brand":"C. T. H. Baker","offers":[{"title":"Paperback","offer_id":47421800743167,"sku":"9780444506009","price":133.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_d7a8ca2e-969d-4f05-91f5-6ab5049cf7a0.jpg?v=1761527200","url":"https:\/\/www.whiterainbookhouse.com\/products\/ordinary-differential-equations-and-integral-c-t-h-baker-9780444506009","provider":"WR Book House","version":"1.0","type":"link"}