Polynomial Approximation of Differential Equations. 1st ed. 1992

種類:

電子ブック

責任表示:

by Daniele Funaro

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992

著者名:

• Funaro, Daniele.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Physics Monographs ; 8

ISBN:

9783540467830 [3540467831]    

注記:

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.
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 colle

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