Overview
- Covers the whole spectrum of partial differential equations, from modeling, analysis, to numerical analysis with numerical illustrations
- Covers the major deterministic numerical methods used in scientific computing practice
- Mathematically self-contained
- Includes supplementary material: sn.pub/extras
Part of the book series: International Series of Numerical Mathematics (ISNM, volume 168)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.
Reviews
“This textbook covers a broad array of aspects of partial differential equations (PDEs), ranging from a study of their analytical properties to the approximate numerical simulations of their solutions. The level of the book is mainly targeted towards Master’s students in applied mathematics or related fields of engineering. … The topics on modeling and approximating partial differential equations are well chosen and are presented in a logical and balanced order.” (Michael M. Tung, Mathematical Reviews, June, 2017)
“This work explores the field of partial differential equations in an advanced manner. … authors provide remarks that help clarify and expand on information that was proved. This is a useful feature for the student trying to make connections with the material. … the authors not only provide a brief summary of the material just covered, but also allude to how this material will be seen in the following chapters. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (S. L. Sullivan, Choice, Vol. 54 (9), May, 2017)
“This book presents both a theoretical and a numerical approach to partial differential equations. … The book appeals to graduate students as well as to researchers in any field of pure and applied mathematics who want to be introduced to numerical approximation method for PDEs through a rigorous approach.” (Marius Ghergu, zbMATH 1339.35005, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Partial Differential Equations: Modeling, Analysis and Numerical Approximation
Authors: Hervé Le Dret, Brigitte Lucquin
Series Title: International Series of Numerical Mathematics
DOI: https://doi.org/10.1007/978-3-319-27067-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-27065-4Published: 19 February 2016
Softcover ISBN: 978-3-319-80066-0Published: 30 March 2018
eBook ISBN: 978-3-319-27067-8Published: 11 February 2016
Series ISSN: 0373-3149
Series E-ISSN: 2296-6072
Edition Number: 1
Number of Pages: XI, 395
Number of Illustrations: 21 b/w illustrations, 119 illustrations in colour
Topics: Partial Differential Equations