# Polynomial Approximation of Differential Equations

• Daniele Funaro
Book

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 8)

1. Front Matter
Pages I-X
2. Pages 1-20
3. Pages 21-34
4. Pages 35-63
5. Pages 65-76
6. Pages 77-92
7. Pages 93-124
8. Pages 125-150
9. Pages 151-180
10. Pages 181-220
11. Pages 221-248
12. Pages 249-264
13. Pages 265-280
14. Pages 281-291
15. Back Matter
Pages 293-305

### Introduction

This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap­ plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be­ ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com­ prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.

### Keywords

Analysis of Convergence Approximationstheorie Boundary-Value Problems Numerical Linear Algebra Numerical integration Numerische Linearalgebra Spectral Methods Spektralmethoden algorithms approximation theory boundary value problem differential equation eigenvalue ordinary differential equation solution

#### Authors and affiliations

• Daniele Funaro
• 1
1. 1.Dipartimento di MatematicaUniversità degli StudiPaviaItaly

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-540-46783-0
• Copyright Information Springer Berlin Heidelberg 1992
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-55230-7
• Online ISBN 978-3-540-46783-0
• Series Print ISSN 0940-7677
• Buy this book on publisher's site
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