EMS Series of Lectures in Mathematics 2010; 236 pp; softcover Volume: 11 ISBN10: 3037190787 ISBN13: 9783037190784 List Price: US$48 Member Price: US$38.40 Order Code: EMSSERLEC/11
 Operator 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 convectiondiffusion equations. Common for these equations is the prevalence of rough, or nonsmooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semidiscrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convectiondiffusion 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. ® MATLAB, The MathWorks, Inc., Natick, MA. Readership Graduate students and research mathematicians interested in partial differential equations. Table of Contents  Introduction
 Simple examples of semidiscrete operator splitting
 General convergence theory
 Convergence results for convectiondiffusion problems
 Error estimates for hyperbolic problems
 Operator splitting for systems of equations
 A. A crash course in numerical methods for conservation laws
 References
 Index
