LEADER 03198oam 2200469 450 001 9910299975703321 005 20190911103511.0 010 $a1-4471-5460-6 024 7 $a10.1007/978-1-4471-5460-0 035 $a(OCoLC)863823003 035 $a(MiFhGG)GVRL6XWI 035 $a(EXLCZ)992550000001151458 100 $a20131018d2014 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis of finite difference schemes $efor linear partial differential equations with generalized solutions /$fBosko S. Jovanovic, Endre Suli 205 $a1st ed. 2014. 210 1$aLondon :$cSpringer,$d2014. 215 $a1 online resource (xiii, 408 pages) $cillustrations 225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v46 300 $a"ISSN: 0179-3632." 311 $a1-4471-5459-2 320 $aIncludes bibliographical references and index. 327 $aDistributions and function spaces -- Elliptic boundary-value problems -- Finite difference approximation of parabolic problems -- Finite difference approximation of hyperbolic problems. 330 $aThis book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary ? and initial ? value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations. 410 0$aSpringer series in computational mathematics ;$v46. 606 $aBoundary value problems 606 $aDifferential equations, Partial$xNumerical solutions 615 0$aBoundary value problems. 615 0$aDifferential equations, Partial$xNumerical solutions. 676 $a515.353 700 $aJovanovi?$b Bo?ko S$4aut$4http://id.loc.gov/vocabulary/relators/aut$0524657 702 $aSuli$b Endre$f1956- 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910299975703321 996 $aAnalysis of Finite Difference Schemes$92512149 997 $aUNINA