Overview
- Surveys both analytical and numerical aspects of hyperbolic balance laws (including the recent theory of viscosity solutions for systems)
- Numerous derivations of both well-balanced and asymptotic-preserving schemes emphasizing relations between each other Includes original material about K-multibranch solutions for linear geometric optics or order-preserving strings
- Several chapters about numerical approximation of chemotaxis or semiconductor kinetic models which display constant macroscopic fluxes at stationary state ("qualitatively correct" approximations)
- Presents well-balanced techniques for linearized Boltzmann and Fokker-Planck kinetic equations
- Includes supplementary material: sn.pub/extras
Part of the book series: SEMA SIMAI Springer Series (SEMA SIMAI, volume 2)
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Table of contents (16 chapters)
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Introduction and Chronological Perspective
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Hyperbolic Quasi-Linear Balance Laws
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Weakly Nonlinear Kinetic Equations
Reviews
From the reviews:
“The overall goal of the book is therefore to explain how to derive accurate numerical approximations of solutions to balance laws. … Each chapter includes comments and historical notes, as well as a list of references. … should be of interest to researchers willing to learn well-balanced techniques.” (Jean-François Coulombel, Mathematical Reviews, January, 2014)
“This book under review gives a systematized and impressive account of the research of the author … written in a well understandable English with some Romanic flavour and featured by a large amount of physical details in this mathematical text, and of pictures showing computing results, often in colours. … a book interesting for mathematical researchers in partial differential equations and for physicist, bringing a wealth of fresh ideas and methods much improving the time splitting approach.” (Gisbert Stoyan, zbMATH, Vol. 1272, 2013)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Computing Qualitatively Correct Approximations of Balance Laws
Book Subtitle: Exponential-Fit, Well-Balanced and Asymptotic-Preserving
Authors: Laurent Gosse
Series Title: SEMA SIMAI Springer Series
DOI: https://doi.org/10.1007/978-88-470-2892-0
Publisher: Springer Milano
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Italia 2013
Hardcover ISBN: 978-88-470-2891-3Published: 22 January 2013
Softcover ISBN: 978-88-470-5855-2Published: 23 August 2016
eBook ISBN: 978-88-470-2892-0Published: 30 March 2013
Series ISSN: 2199-3041
Series E-ISSN: 2199-305X
Edition Number: 1
Number of Pages: XIX, 341
Topics: Computational Mathematics and Numerical Analysis, Partial Differential Equations, Applications of Mathematics, Mathematical and Computational Engineering, Numerical and Computational Physics, Simulation
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