Polynominal Approximation of Differential Equations: 8 (Lecture Notes in Physics Monographs) - Hardcover

Funaro, Daniele

Hardcover

ISBN 10: 3540552308 ISBN 13: 9783540552307

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

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.

About this title

Synopsis

This book is a basic and comprehensive introduction to the use of spectral methods for the approximation of the solution to ordinary differential equations and time-dependent boundary-value problems. The algorithms are presented and studied both from the point of view of the theoretical analysis of convergence and the numerical implementation.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1992
• ISBN 10: 3540552308
• ISBN 13: 9783540552307
• Binding: Hardcover
• Language: English
• Number of pages: 315