
Polynomial Approximation of Differential Equations
Daniele Funaro(Author)
Springer (Publisher)
Published on 23. August 2014
Book
Paperback/Softback
X, 305 pages
978-3-662-13878-6 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1992
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
3 s/w Abbildungen
X, 305 p. 3 illus.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 18 mm
Weight
555 gr
ISBN-13
978-3-662-13878-6 (9783662138786)
DOI
10.1007/978-3-540-46783-0
Schweitzer Classification
Other editions
Additional editions
Daniele Funaro
Polynomial Approximation of Differential Equations
Book
04/1992
Springer
€85.59
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Content
Special Families of Polynomials.- Orthogonality.- Numerical Integration.- Transforms.- Functional Spaces.- Results in Approximation Theory.- Derivative Matrices.- Eigenvalue Analysis.- Ordinary Differential Equations.- Time-Dependent Problems.- Domain-Decomposition Methods.- Examples.- An Example in Two Dimensions.