偏微分方程式：モデル化、解析、数値的近似（テキスト） Partial Differential Equations: Modeling, Analysis and Numerical Approximation (International Series of Numerical Mathematics)

Le Dret, Hervé/ Lucquin, Brigitte

Birkhauser Verlag AG（2016/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 395 p.
• 商品コード 9783319270654

Full Description

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.

 

Contents

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.