000 03142nam a22004695i 4500
001 978-3-0348-0107-2
003 DE-He213
005 20140220083739.0
007 cr nn 008mamaa
008 110810s2011 sz | s |||| 0|eng d
020 _a9783034801072
_9978-3-0348-0107-2
024 7 _a10.1007/978-3-0348-0107-2
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.352
_223
100 1 _aGavrilyuk, Ivan.
_eauthor.
245 1 0 _aExact and Truncated Difference Schemes for Boundary Value ODEs
_h[electronic resource] /
_cby Ivan Gavrilyuk, Martin Hermann, Volodymyr Makarov, Myroslav V. Kutniv.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _aXII, 248 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInternational Series of Numerical Mathematics ;
_v159
505 0 _aPreface -- 1 Introduction and a short historical overview -- 2 2-point difference schemes for systems of ODEs -- 3 3-point difference schemes for scalar monotone ODEs -- 4 3-point difference schemes for systems of monotone ODEs -- 5 Difference schemes for BVPs on the half-axis -- 6 Exercises and solutions -- Index.
520 _aThe book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems. The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.
650 0 _aMathematics.
650 0 _aDifferential Equations.
650 1 4 _aMathematics.
650 2 4 _aOrdinary Differential Equations.
700 1 _aHermann, Martin.
_eauthor.
700 1 _aMakarov, Volodymyr.
_eauthor.
700 1 _aKutniv, Myroslav V.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034801065
830 0 _aInternational Series of Numerical Mathematics ;
_v159
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0107-2
912 _aZDB-2-SMA
999 _c106595
_d106595