000 | 03248nam a22005055i 4500 | ||
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001 | 978-3-319-11445-3 | ||
003 | DE-He213 | ||
005 | 20190213151057.0 | ||
007 | cr nn 008mamaa | ||
008 | 141013s2014 gw | s |||| 0|eng d | ||
020 |
_a9783319114453 _9978-3-319-11445-3 |
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024 | 7 |
_a10.1007/978-3-319-11445-3 _2doi |
|
050 | 4 | _aQA247-QA247.45 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002010 _2bisacsh |
|
072 | 7 |
_aPBF _2thema |
|
082 | 0 | 4 |
_a512.3 _223 |
100 | 1 |
_aRobertz, Daniel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aFormal Algorithmic Elimination for PDEs _h[electronic resource] / _cby Daniel Robertz. |
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2014. |
|
300 |
_aVIII, 283 p. 6 illus., 3 illus. in color. _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 |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2121 |
|
505 | 0 | _aIntroduction -- Formal Methods for PDE Systems -- Differential Elimination for Analytic Functions -- Basic Principles and Supplementary Material -- References -- List of Algorithms -- List of Examples -- Index of Notation -- Index. | |
520 | _aInvestigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed. | ||
650 | 0 | _aField theory (Physics). | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aDifferential equations, partial. | |
650 | 1 | 4 |
_aField Theory and Polynomials. _0http://scigraph.springernature.com/things/product-market-codes/M11051 |
650 | 2 | 4 |
_aCommutative Rings and Algebras. _0http://scigraph.springernature.com/things/product-market-codes/M11043 |
650 | 2 | 4 |
_aAssociative Rings and Algebras. _0http://scigraph.springernature.com/things/product-market-codes/M11027 |
650 | 2 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319114460 |
776 | 0 | 8 |
_iPrinted edition: _z9783319114446 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2121 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-11445-3 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c9436 _d9436 |