Partial Differential Equations: Modeling, Analysis and Numerical Approximation

AvHervé Le Dret,Brigitte Lucquin

Inbunden, Engelska, 2016

Del i serien International Series of Numerical Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-02-19
Mått:155 x 235 x 28 mm
Vikt:776 g
Format:Inbunden
Språk:Engelska
Serie:International Series of Numerical Mathematics
Antal sidor:395
Upplaga:16001
Förlag:Birkhauser Verlag AG
ISBN:9783319270654

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"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)

Innehållsförteckning

Foreword.- Mathematical modeling and PDEs.- The finite difference method for elliptic problems.- A review of analysis.- The variational formulation of elliptic PDEs.-Variational approximation methods for elliptic PDEs.- The finite element method in dimension two.- The heat equation.- The finite difference method for the heat equation.- The wave equation.- The finite volume method.- Index.- References.