LEADER 03719nam 2200757 450 001 9910790824503321 005 20230803220633.0 010 $a3-11-032146-7 024 7 $a10.1515/9783110321463 035 $a(CKB)2550000001169830 035 $a(EBL)1563353 035 $a(OCoLC)865330717 035 $a(SSID)ssj0001060531 035 $a(PQKBManifestationID)11634088 035 $a(PQKBTitleCode)TC0001060531 035 $a(PQKBWorkID)11088081 035 $a(PQKB)10045587 035 $a(MiAaPQ)EBC1563353 035 $a(DE-B1597)210800 035 $a(OCoLC)979906440 035 $a(DE-B1597)9783110321463 035 $a(Au-PeEL)EBL1563353 035 $a(CaPaEBR)ebr10820026 035 $a(CaONFJC)MIL551815 035 $a(EXLCZ)992550000001169830 100 $a20130725h20142014 uy| 0 101 0 $aeng 135 $aurun#---|uu|u 181 $ctxt 182 $cc 183 $acr 200 10$aAdditive operator-difference schemes $esplitting schemes /$fby Petr N. Vabishchevich 210 1$aBerlin ;$aBoston :$cWalter de Gruyter GmbH & Co. KG,$d[2014] 210 4$dİ2014 215 $a1 online resource (370 p.) 300 $aDescription based upon print version of record. 311 0 $a3-11-032143-2 311 0 $a1-306-20564-6 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tNotation --$t1. Introduction --$t2. Stability of operator-difference schemes --$t3. Operator splitting --$t4. Additive schemes of two-component splitting --$t5. Schemes of summarized approximation --$t6. Regularized additive schemes --$t7. Schemes based on approximations of a transition operator --$t8. Vector additive schemes --$t9. Iterative methods --$t10. Splitting of the operator at the time derivative --$t11 Equations with pairwise adjoint operators --$tBibliography --$tIndex 330 $aApplied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner. 606 $aInitial value problems 606 $aBoundary value problems 606 $aDifferential operators 606 $aMathematical models 610 $aIterative Methods. 610 $aOperator Splitting. 610 $aRegularized Additive Schemes. 610 $aSummarized Approximation. 610 $aTransition Operator Approximations. 610 $aTwo-Component Splitting. 610 $aVector Additive Schemes. 615 0$aInitial value problems. 615 0$aBoundary value problems. 615 0$aDifferential operators. 615 0$aMathematical models. 676 $a515/.724 686 $aSK 920$2rvk 700 $aVabishchevich$b P. N$g(Petr Nikolaevich)$067879 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910790824503321 996 $aAdditive operator-difference schemes$93697798 997 $aUNINA