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Polynomial Approximation of Differential Equations

  • Book
  • © 1992

Overview

Authors:
  1. Daniele Funaro

    1. Dipartimento di Matematica, Università degli Studi, Pavia, Italy

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

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About this book

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.

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Special Families of Polynomials

    Pages 1-20

  3. Orthogonality

    Pages 21-34

  4. Numerical Integration

    Pages 35-63

  5. Transforms

    Pages 65-76

  6. Functional Spaces

    Pages 77-92

  7. Results in Approximation Theory

    Pages 93-124

  8. Derivative Matrices

    Pages 125-150

  9. Eigenvalue Analysis

    Pages 151-180

  10. Ordinary Differential Equations

    Pages 181-220

  11. Time-Dependent Problems

    Pages 221-248

  12. Domain-Decomposition Methods

    Pages 249-264

  13. Examples

    Pages 265-280

  14. An Example in Two Dimensions

    Pages 281-291

  15. Back Matter

    Pages 293-305
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Authors and Affiliations

  • Dipartimento di Matematica, Università degli Studi, Pavia, Italy

    Daniele Funaro

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