Partial differential equations with numerical methods

Stig Larsson, Vidar Thomée

268 pages, parution le 08/09/2003

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Résumé

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Introduction
A two-point boundary value problem
Elliptic equations
Finite difference methods for elliptic equations
Finite element methods for elliptic equations
The elliptic eigenvalue problem
Initial-value problems for ODEs
Parabolic equations
Finite difference methods for parabolic problems
The finite element method for a parabolic problem
Hyperbolic equations
Finite difference methods for hyperbolic equations
The finite element method for hyperbolic equations
Some other classes of numerical methods
Some tools from mathematical analysis
Orientation on numerical linear algebra
Bibliography
Index

L'auteur - Stig Larsson

Stig Larsson - Chalmers University of Technology and Göteborg University, Göteborg, Sweden;

L'auteur - Vidar Thomée

Chalmers University of Technology and Göteborg University, Göteborg, Sweden.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Stig Larsson, Vidar Thomée
Parution	08/09/2003
Nb. de pages	268
Format	16 x 24
Couverture	Relié
Poids	525g
Intérieur	Noir et Blanc
EAN13	9783540017721