Polynomial Approximation of Differential Equations

Daniele Funaro

ISBN 10: 3662138786 / ISBN 13: 9783662138786

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2014, 2014

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 320 pp. Englisch.

Seller Inventory # 9783662138786

Bibliographic Details

• Title: Polynomial Approximation of Differential Equations
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2014
• Publication Date: 2014
• Language: English
• ISBN 10: 3662138786
• ISBN 13: 9783662138786
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.