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Holden H., Karlsen K. — Splitting Methods for Partial Differential Equations With Rough Solutions: Analysis and Matlabr Programs
Holden H., Karlsen K. — Splitting Methods for Partial Differential Equations With Rough Solutions: Analysis and Matlabr Programs

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Название: Splitting Methods for Partial Differential Equations With Rough Solutions: Analysis and Matlabr Programs

Авторы: Holden H., Karlsen K.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Неизвестно

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Год издания: 2010

Количество страниц: 235

Добавлена в каталог: 26.02.2014

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