LEADER 02965nam 22004935a 450 001 9910151932203321 005 20100420234500.0 010 $a3-03719-578-9 024 70$a10.4171/078 035 $a(CKB)3710000000953853 035 $a(CH-001817-3)112-100420 035 $a(PPN)17815573X 035 $a(EXLCZ)993710000000953853 100 $a20100420j20100430 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSplitting Methods for Partial Differential Equations with Rough Solutions$b[electronic resource] $eAnalysis and MATLAB programs /$fHelge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik Risebro 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2010 215 $a1 online resource (234 pages) 225 0 $aEMS Series of Lectures in Mathematics (ELM) ;$x2523-5176 330 $aOperator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated web page that provides MATLAB codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering. 606 $aDifferential equations$2bicssc 606 $aNumerical analysis$2bicssc 606 $aNumerical analysis$2msc 606 $aPartial differential equations$2msc 606 $aOperator theory$2msc 615 07$aDifferential equations 615 07$aNumerical analysis 615 07$aNumerical analysis 615 07$aPartial differential equations 615 07$aOperator theory 686 $a65-xx$a35-xx$a47-xx$2msc 700 $aHolden$b Helge$052245 702 $aKarlsen$b Kenneth Hvistendahl 702 $aLie$b Knut-Andreas 702 $aRisebro$b Nils Henrik 801 0$bch0018173 906 $aBOOK 912 $a9910151932203321 996 $aSplitting methods for partial differential equations with rough solutions$9762630 997 $aUNINA