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Titlebook: Difference Schemes with Operator Factors; A. A. Samarskii,P. P. Matus,P. N. Vabishchevich Book 2002 Springer Science+Business Media Dordre

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發(fā)表于 2025-3-21 18:20:54 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Difference Schemes with Operator Factors
編輯A. A. Samarskii,P. P. Matus,P. N. Vabishchevich
視頻videohttp://file.papertrans.cn/279/278616/278616.mp4
叢書(shū)名稱Mathematics and Its Applications
圖書(shū)封面Titlebook: Difference Schemes with Operator Factors;  A. A. Samarskii,P. P. Matus,P. N. Vabishchevich Book 2002 Springer Science+Business Media Dordre
描述Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non- stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta- bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di- rections. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tad- more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu- tion to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem f
出版日期Book 2002
關(guān)鍵詞Mathematica; computational mathematics; finite element method; numerical method; operator; problem solvin
版次1
doihttps://doi.org/10.1007/978-94-015-9874-3
isbn_softcover978-90-481-6118-8
isbn_ebook978-94-015-9874-3
copyrightSpringer Science+Business Media Dordrecht 2002
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沙發(fā)
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th respect to the space variables, are often used to solve numerically non- stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta- bility of a difference solution (or well posedness of a difference scheme) wit
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Two-Level Difference Schemes,he Cauchy problem for a system of ordinary differential equations which is considered in a Hilbert grid space. The discretisation in time yields an operator-difference scheme. Let us mention some most important directions in the development of the theory of operator-difference schemes for nonstationary problems of mathematical physics.
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Difference Schemes for Non-Stationary Equations,analysis of numerical methods. The stability of difference schemes for linear problems with respect to the initial data and the right hand side, and also coefficient (strong) stability ensure the well posedness of a discrete problem, in other words, its right to exist.
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Difference Schemes of Domain Decomposition for Non-Stationary Problems,in regular simpler domains. The first of them (the method of fictitious domains) is based on imbedding the original irregular domain into a regular domain with some continuations of the coefficients of the original equation into the adjoining domain and corresponding choice of boundary conditions on the boundary of the extended domain.
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