Splitting methods for partial differential equations with rough solutions
[Book]
:analysis and MATLAB programs
/ Helge Holden ... [et al.]
Zeurich
: European Mathematical Society ;[Providence, R.I. :Distributed within the Americas by the American Mathematical Society],
, c2010.
viii, 226 p. , ill. , 24 cm.
(EMS series of lectures in mathematics)
Electronic
Includes bibliographical references (p. [201]-223) and index.
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.