000 | 03365nam a22004575i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-540-74993-6 _2doi |
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050 | 4 | _aQA71-90 | |
072 | 7 |
_aPBKS _2bicssc |
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072 | 7 |
_aMAT006000 _2bisacsh |
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082 | 0 | 4 |
_a518 _223 |
100 | 1 |
_aGustafsson, Bertil. _eauthor. |
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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. |
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300 |
_aXVI, 334 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSpringer Series in Computational Mathematics, _x0179-3632 ; _v38 |
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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 |