Partial Differential Equations: Modeling, Analysis and Numerical Approximation

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book Partial Differential Equations: Modeling, Analysis and Numerical Approximation by Hervé Le Dret, Brigitte Lucquin, Springer International Publishing
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Author: Hervé Le Dret, Brigitte Lucquin ISBN: 9783319270678
Publisher: Springer International Publishing Publication: February 11, 2016
Imprint: Birkhäuser Language: English
Author: Hervé Le Dret, Brigitte Lucquin
ISBN: 9783319270678
Publisher: Springer International Publishing
Publication: February 11, 2016
Imprint: Birkhäuser
Language: English

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.

 

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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.

 

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