000 03365nam a22004575i 4500
001 978-3-540-74993-6
003 DE-He213
005 20161121231214.0
007 cr nn 008mamaa
008 100301s2008 gw | s |||| 0|eng d
020 _a9783540749936
_9978-3-540-74993-6
024 7 _a10.1007/978-3-540-74993-6
_2doi
050 4 _aQA71-90
072 7 _aPBKS
_2bicssc
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aGustafsson, Bertil.
_eauthor.
245 1 0 _aHigh Order Difference Methods for Time Dependent PDE
_h[electronic resource] /
_cby Bertil Gustafsson.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXVI, 334 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Computational Mathematics,
_x0179-3632 ;
_v38
505 0 _aWhen 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.
520 _aMany 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.
650 0 _aMathematics.
650 0 _aPartial differential equations.
650 0 _aComputer mathematics.
650 1 4 _aMathematics.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540749929
830 0 _aSpringer Series in Computational Mathematics,
_x0179-3632 ;
_v38
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-74993-6
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c510112
_d510112