---

＜電子ブック＞
Analysis of Discretization Methods for Ordinary Differential Equations / by Hans J. Stetter
(Springer Tracts in Natural Philosophy ; 23)

版	1st ed. 1973.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1973
本文言語	英語
大きさ	XVI, 390 p : online resource
著者標目	*Stetter, Hans J author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical analysis FREE:Differential Equations FREE:Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-65471-8

 類似資料