000 03033nam a22004935i 4500
001 978-3-7091-1286-1
003 DE-He213
005 20140220083332.0
007 cr nn 008mamaa
008 120928s2012 au | s |||| 0|eng d
020 _a9783709112861
_9978-3-7091-1286-1
024 7 _a10.1007/978-3-7091-1286-1
_2doi
050 4 _aQA76.9.M35
072 7 _aUYAM
_2bicssc
072 7 _aCOM018000
_2bisacsh
072 7 _aMAT002000
_2bisacsh
082 0 4 _a005.131
_223
100 1 _aSchwarz, Fritz.
_eauthor.
245 1 0 _aLoewy Decomposition of Linear Differential Equations
_h[electronic resource] /
_cby Fritz Schwarz.
264 1 _aVienna :
_bSpringer Vienna :
_bImprint: Springer,
_c2012.
300 _aXV, 230 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x0943-853X
505 0 _aLoewy's results for ordinary differential equations -- Rings of partial differential operators -- Equations with finite-dimensional solution space -- Decomposition of second-order operators -- Solving second-order equations -- Decomposition of third-order operators -- Solving third-order equations -- Summary and conclusions -- Solutions to the exercises -- Solving Riccati equations -- The method of Laplace -- Equations with Lie symmetries.
520 _aThe central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.
650 0 _aComputer science.
650 0 _aAlgebra
_xData processing.
650 0 _aDifferential equations, partial.
650 0 _aEngineering mathematics.
650 1 4 _aComputer Science.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aPartial Differential Equations.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783709112854
830 0 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x0943-853X
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7091-1286-1
912 _aZDB-2-SCS
999 _c103937
_d103937