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Titlebook: Analysis of Discretization Methods for Ordinary Differential Equations; Hans J. Stetter Book 1973 Springer-Verlag Berlin Heidelberg 1973 A

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期刊全稱Analysis of Discretization Methods for Ordinary Differential Equations
影響因子2023Hans J. Stetter
視頻videohttp://file.papertrans.cn/157/156349/156349.mp4
學(xué)科分類Springer Tracts in Natural Philosophy
圖書封面Titlebook: Analysis of Discretization Methods for Ordinary Differential Equations;  Hans J. Stetter Book 1973 Springer-Verlag Berlin Heidelberg 1973 A
影響因子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 num
Pindex Book 1973
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Linear Multistep Methods,ecial class of one-stage .-step methods whose forward-step procedures consist simply of a . combination of values of . and . (.) at . + 1 consecutive gridpoints ., .= . ?.(1).. No re-sub-stitutions into . (which formed the essence of RK-methods) will be permitted. Even with these limitations, this s
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Other Discretization Methods for IVP 1, computation of values of higher derivatives of the local solution of an IVP 1 is feasible for large classes of IVP 1. In Section 6.1, we will survey some of the principal approaches which yield f. s. m. using such higher derivatives.
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Springer Tracts in Natural Philosophyhttp://image.papertrans.cn/a/image/156349.jpg
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https://doi.org/10.1007/978-3-662-28855-9In initial-value problems for ordinary differential equations the independent variable is commonly interpreted as . and the vector of unknown functions as a state vector varying in time. Given the state at one time instant ., the desired solution consists of the state vectors during some time interval [., . + .].
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Analysis of Discretization Methods for Ordinary Differential Equations978-3-642-65471-8Series ISSN 0081-3877
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Caroline Gr?schner,Kerstin Jergus computation of values of higher derivatives of the local solution of an IVP 1 is feasible for large classes of IVP 1. In Section 6.1, we will survey some of the principal approaches which yield f. s. m. using such higher derivatives.
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