02965nam 22004935a 450 991015193220332120100420234500.03-03719-578-910.4171/078(CKB)3710000000953853(CH-001817-3)112-100420(PPN)17815573X(EXLCZ)99371000000095385320100420j20100430 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierSplitting Methods for Partial Differential Equations with Rough Solutions[electronic resource] Analysis and MATLAB programs /Helge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik RisebroZuerich, Switzerland European Mathematical Society Publishing House20101 online resource (234 pages)EMS Series of Lectures in Mathematics (ELM) ;2523-5176Operator 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.Differential equationsbicsscNumerical analysisbicsscNumerical analysismscPartial differential equationsmscOperator theorymscDifferential equationsNumerical analysisNumerical analysisPartial differential equationsOperator theory65-xx35-xx47-xxmscHolden Helge52245Karlsen Kenneth HvistendahlLie Knut-AndreasRisebro Nils Henrikch0018173BOOK9910151932203321Splitting methods for partial differential equations with rough solutions762630UNINA