Splitting Methods for Partial Differential Equations with Rough Solutions: Analysis and Matlab Programs (EMS Series of Lectures in Mathematics) - Softcover

Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas

Softcover

ISBN 10: 3037190787 ISBN 13: 9783037190784

Publisher: European Mathematical Society, 2010

Synopsis

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 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 tacking. 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.

Edition details

• Publisher: European Mathematical Society
• Publication date: 2010
• Language: English
• ISBN 10: 3037190787
• ISBN 13: 9783037190784
• Binding: Paperback
• Number of pages: 236