# Splitting Methods for Partial Differential Equations with Rough Solutions: Analysis and MATLAB® Programs

Share this page
*Helge Holden; Kenneth H. Karlsen; Knut-Andreas Lie; Nils Henrik Risebro*

A publication of the European Mathematical Society

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
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.

#### Readership

Graduate students and research mathematicians interested in partial differential equations.