Partial Differential Equations: Modeling
β HervΓΒ© Le Dret, Brigitte Lucquin
π Library
π
2016
π BirkhΓΒ€user
π English
β¦ LIBER β¦
π
Partial Differential Equations: Modeling, Analysis and Numerical Approximation
β Scribed by HervΓ© Le Dret, Brigitte Lucquin (auth.)
- Publisher
- BirkhΓ€user Basel
- Year
- 2016
- Tongue
- English
- Leaves
- 403
- Series
- International Series of Numerical Mathematics 168
- Edition
- 1
- Category
- Library
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No coin nor oath required. For personal study only.
β¦ Synopsis
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.
β¦ Table of Contents
Front Matter....Pages i-xi
Mathematical Modeling and PDEs....Pages 1-34
The Finite Difference Method for Elliptic Problems....Pages 35-67
A Review of Analysis....Pages 69-116
The Variational Formulation of Elliptic PDEs....Pages 117-143
Variational Approximation Methods for Elliptic PDEs....Pages 145-166
The Finite Element Method in Dimension Two....Pages 167-218
The Heat Equation....Pages 219-251
The Finite Difference Method for the Heat Equation....Pages 253-305
The Wave Equation....Pages 307-344
The Finite Volume Method....Pages 345-382
Back Matter....Pages 383-395
β¦ Subjects
Partial Differential Equations
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