| Document Type
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BL
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| Record Number
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752150
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| Doc. No
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b572109
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| Main Entry
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[by] Hans J. Stetter.
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| Title & Author
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Analysis of discretization methods for ordinary differential equations\ [by] Hans J. Stetter.
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| Publication Statement
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Berlin: New York, Springer, 1973
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| Series Statement
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Springer tracts in natural philosophy, v. 23.
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| Page. NO
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(xvi, 388 pages) 12 graphs
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| ISBN
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3642654711
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: 9783642654718
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| Contents
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1 General Discretization Methods --; 1.1. Basic Definitions --; 1.2 Results Concerning Stability --; 1.3 Asymptotic Expansions of the Discretization Errors --; 1.4 Applications of Asymptotic Expansions --; 1.5 Error Analysis --; 1.6 Practical Aspects --; 2 Forward Step Methods --; 2.1 Preliminaries --; 2.2 The Meaning of Consistency, Convergence, and Stability with Forward Step Methods --; 2.3 Strong Stability of f.s.m. --; 3 Runge-Kutta Methods --; 3.1 RK-procedures --; 3.2 The Group of RK-schemes --; 3.3 RK-methods and Their Orders --; 3.4 Analysis of the Discretization Error --; 3.5 Strong Stability of RK-methods --; 4 Linear Multistep Methods --; 4.1 Linear k-step Schemes --; 4.2 Uniform Linear k-step Methods --; 4.3 Cyclic Linear k-step Methods --; 4.4 Asymptotic Expansions --; 4.5 Further Analysis of the Discretization Error --; 4.6 Strong Stability of Linear Multistep Methods --; 5 Multistage Multistep Methods --; 5.1 General Analysis --; 5.2 Predictor-corrector Methods --; 5.3 Predictor-corrector Methods with Off-step Points --; 5.4 Cyclic Forward Step Methods --; 5.5 Strong Stability --; 6 Other Discretization Methods for IVP 1 --; 6.1 Discretization Methods with Derivatives of f --; 6.2 General Multi-value Methods --; 6.3 Extrapolation Methods.
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| Abstract
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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℗Ư difference methods have been known for a long time, their wide applica℗Ư 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℗Ư book by page.
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| Subject
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Difference equations -- Numerical solutions.
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| Subject
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Differential equations -- Numerical solutions.
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| Subject
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Gewöhnliche Differentialgleichung
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| Added Entry
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Hans J Stetter
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