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eebo-0018
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7-Volume Set now available at special set price ! 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 "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 ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step 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 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 Problem Solving Environments?" Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the n th 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 Runge-Kutta 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. St
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This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems. The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text and it allows a thorough account to be given of many of the types of integral equation which arise in application areas. Since it is not always possible to find explicit solutions of the problems posed, much attention is devoted to obtaining qualitative information and approximations to the solutions, with the associated error estimates. This treatment is intended for final year mathematics undergraduates, postgraduates and research workers in application areas such as numerical analysis and fluid mechanics.
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Equations. --- Equations --- Algebra --- Mathematics
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