Hans J. Stetter – författare
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3 produkter
3 produkter
1 479 kr
Skickas inom 5-8 vardagar
538 kr
Skickas inom 10-15 vardagar
This computing supplementum collects a number of original contributions which all aim to compute rigorous and reliable error bounds for the solution of numerical problems. An introductory article by the editors about the meaning and diverse methods of automatic result verification is followed by 16 original contributions. The first chapter deals with automatic result verification for standard mathematical problems, such as enclosing the solution of ordinary boundary value problems, linear programming problems, linear systems of equations and eigenvalue problems. The second chapter deals with applications of result verification methods to problems of the technical sciences. The contributions consider critical bending vibrations stability tests for periodic differential equations, geometric algorithms in the plane, and the periodic solution of the oregonator, a mathematical model in chemical kinetics. The contributions of the third chapter are concerned with extending and developing the tools required in scientific computation with automatic result verification.
537 kr
Skickas inom 10-15 vardagar
Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finite difference methods have been known for a long time, their wide applica bility and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P.