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Splitting Methods for Partial Differ...

Holden, Helge,

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Splitting Methods for Partial Differential Equations with Rough Solutions = Analysis and MATLAB programs /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Splitting Methods for Partial Differential Equations with Rough Solutions/ Helge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik Risebro
Reminder of title:	Analysis and MATLAB programs /
Author:	Holden, Helge,
other author:	Karlsen, Kenneth Hvistendahl,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2010,
Description:	1 online resource (234 pages)
Subject:	Differential equations -
Online resource:	https://doi.org/10.4171/078
Online resource:	https://www.ems-ph.org/img/books/holden_mini.jpg
ISBN:	9783037195789

Splitting Methods for Partial Differential Equations with Rough Solutions = Analysis and MATLAB programs /
Holden, Helge,

Splitting Methods for Partial Differential Equations with Rough SolutionsAnalysis and MATLAB programs /[electronic resource] :Helge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik Risebro - Zuerich, Switzerland :European Mathematical Society Publishing House,2010 - 1 online resource (234 pages) - EMS Series of Lectures in Mathematics (ELM) ;2523-5176.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037195789

Standard No.: 10.4171/078doiSubjects--Topical Terms:

704075
Differential equations

Splitting Methods for Partial Differential Equations with Rough Solutions = Analysis and MATLAB programs /
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520 $a 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.
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700 1 $a Lie, Knut-Andreas, $e author. $3 3480977
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