02842nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001600185084002900201100002800230245021700258260008200475300003400557336002600591337002600617338003600643347002400679490006100703506006600764520122300830650003502053650003102088650002802119650004002147650002502187700004302212700003202255700003502287856003202322856006602354112-100420CH-001817-320100420234500.0a fot ||| 0|cr nn mmmmamaa100420e20100430sz fot ||| 0|eng d a978303719578970a10.4171/0782doi ach0018173 7aPBKJ2bicssc 7aPBS2bicssc a65-xxa35-xxa47-xx2msc1 aHolden, Helge,eauthor.10aSplitting Methods for Partial Differential Equations with Rough Solutionsh[electronic resource] :bAnalysis and MATLAB programs /cHelge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik Risebro3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (234 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aDifferential equations2bicssc07aNumerical analysis2bicssc07aNumerical analysis2msc07aPartial differential equations2msc07aOperator theory2msc1 aKarlsen, Kenneth Hvistendahl,eauthor.1 aLie, Knut-Andreas,eauthor.1 aRisebro, Nils Henrik,eauthor.40uhttps://doi.org/10.4171/078423cover imageuhttps://www.ems-ph.org/img/books/holden_mini.jpg