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Titlebook: Exact and Truncated Difference Schemes for Boundary Value ODEs; Ivan Gavrilyuk,Martin Hermann,Myroslav V. Kutniv Book 2011 The Editor(s) (

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發(fā)表于 2025-3-21 16:29:17 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Exact and Truncated Difference Schemes for Boundary Value ODEs
編輯Ivan Gavrilyuk,Martin Hermann,Myroslav V. Kutniv
視頻videohttp://file.papertrans.cn/319/318157/318157.mp4
概述Contains the first comprehensive and unified theory of compact finite difference methods for the numerical solution of nonlinear boundary value problems of ordinary differential equations (ODEs).Detai
叢書名稱International Series of Numerical Mathematics
圖書封面Titlebook: Exact and Truncated Difference Schemes for Boundary Value ODEs;  Ivan Gavrilyuk,Martin Hermann,Myroslav V. Kutniv Book 2011 The Editor(s) (
描述.The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems..The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODE
出版日期Book 2011
關鍵詞ordinary differential equations
版次1
doihttps://doi.org/10.1007/978-3-0348-0107-2
isbn_softcover978-3-0348-0341-0
isbn_ebook978-3-0348-0107-2Series ISSN 0373-3149 Series E-ISSN 2296-6072
issn_series 0373-3149
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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沙發(fā)
發(fā)表于 2025-3-21 23:12:17 | 只看該作者
Two-point difference schemes for systems of nonlinear BVPs,f IVPs on small subintervals and are theoretically supported by a posteriori error estimates. However, the advantage of our difference methods is that a unified theory of a priori estimates can be established.
板凳
發(fā)表于 2025-3-22 03:20:17 | 只看該作者
Three-point difference schemes for monotone second-order ODEs,int stencil and prove the existence and uniqueness of its solution. Moreover, on the basis of the EDS we develop an algorithm for the construction of a three-point TDS of rank . is a given natural number and [·] denotes the entire part of the argument in brackets. We prove the existence and uniquene
地板
發(fā)表于 2025-3-22 07:09:13 | 只看該作者
0373-3149 lue problems of ordinary differential equations (ODEs).Detai.The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable trunca
5#
發(fā)表于 2025-3-22 09:17:49 | 只看該作者
https://doi.org/10.1057/9780230355538a three-point TDS of rank . is a given natural number and [·] denotes the entire part of the argument in brackets. We prove the existence and uniqueness of the solution of the TDS and determine the order of accuracy. Numerical examples are given which confirm the theoretical results.
6#
發(fā)表于 2025-3-22 13:28:16 | 只看該作者
7#
發(fā)表于 2025-3-22 19:38:55 | 只看該作者
https://doi.org/10.1057/9781137431677 boundary value problems (BVPs) for systems of nonlinear ordinary differential equations (ODEs). However, it is not possible in general to determine the solution of nonlinear problems in a closed form. Therefore the exact solution must be approximated by numerical techniques.
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發(fā)表于 2025-3-23 09:04:51 | 只看該作者
0373-3149 dy. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODE978-3-0348-0341-0978-3-0348-0107-2Series ISSN 0373-3149 Series E-ISSN 2296-6072
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