Ebook: Numerical Analysis
Author: Roger Temam (auth.)
- Tags: Computational Mathematics and Numerical Analysis, Numeric Computing
- Year: 1973
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
This book is an introduction to one of the important as pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation. This book is not a systematic study of the subject, but the methods developed here can be applied to large classes of linear and nonlinear elliptic problems. The book assumes that the reader's knowledge of Anal ysis is comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.
Content:
Front Matter....Pages I-VIII
Approximate Solution of Functional Equations: General Remarks....Pages 1-2
Front Matter....Pages 3-3
The Projection Theorem....Pages 5-11
The Method of Galerkin....Pages 12-17
The Approximation of Normed Spaces....Pages 18-30
Approximation of Linear Variational Problems....Pages 31-39
A Method for Computation of the Error....Pages 40-42
The Method of Fractionary Steps....Pages 43-49
Front Matter....Pages 51-51
Spaces of Functions Associated with an open set in R n ....Pages 53-58
Approximation of Some Function Spaces by Finite Differences (I)....Pages 59-69
Approximation of Some Function Spaces by Finite Differences (II)....Pages 70-79
Approximation of Some Function Spaces by Finite Element Methods....Pages 80-104
Example I: the Dirichlet Problem....Pages 105-120
Example II: The Neumann Problem....Pages 121-128
Front Matter....Pages 129-129
The Exact Problem....Pages 131-142
Approximate Problems....Pages 143-155
Back Matter....Pages 156-167
Content:
Front Matter....Pages I-VIII
Approximate Solution of Functional Equations: General Remarks....Pages 1-2
Front Matter....Pages 3-3
The Projection Theorem....Pages 5-11
The Method of Galerkin....Pages 12-17
The Approximation of Normed Spaces....Pages 18-30
Approximation of Linear Variational Problems....Pages 31-39
A Method for Computation of the Error....Pages 40-42
The Method of Fractionary Steps....Pages 43-49
Front Matter....Pages 51-51
Spaces of Functions Associated with an open set in R n ....Pages 53-58
Approximation of Some Function Spaces by Finite Differences (I)....Pages 59-69
Approximation of Some Function Spaces by Finite Differences (II)....Pages 70-79
Approximation of Some Function Spaces by Finite Element Methods....Pages 80-104
Example I: the Dirichlet Problem....Pages 105-120
Example II: The Neumann Problem....Pages 121-128
Front Matter....Pages 129-129
The Exact Problem....Pages 131-142
Approximate Problems....Pages 143-155
Back Matter....Pages 156-167
....