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＜電子ブック＞
High Order Difference Methods for Time Dependent PDE / by Bertil Gustafsson
(Springer Series in Computational Mathematics. ISSN:21983712 ; 38)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XVI, 334 p : online resource
著者標目	*Gustafsson, Bertil author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Differential equations FREE:Computational Mathematics and Numerical Analysis FREE:Differential Equations
一般注記	When are High Order Methods Effective? -- Well-posedness and Stability -- Order of Accuracy and the Convergence Rate -- Approximation in Space -- Approximation in Time -- Coupled Space-Time Approximations -- Boundary Treatment -- The Box Scheme -- Wave Propagation -- A Problem in Fluid Dynamics -- Nonlinear Problems with Shocks -- to Other Numerical Methods Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de?nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ?ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful?lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And ?nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial–boundary value problems. The content of the book is not purely theoretical, neither is it a set of recipes for varioustypesof applications. The idea is to give an overviewof the basic theoryand constructionprinciplesfor differencemethodswithoutgoing into all details. For - ample, certain theorems are presented, but the proofs are in most cases left out. The explanation and application of the theory is illustrated by using simple model - amples HTTP:URL=https://doi.org/10.1007/978-3-540-74993-6

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