Polynomial Approximation of Differential Equations

✍ Scribed by Daniele Funaro (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 1992
• Tongue: English
• Leaves: 312
• Series: Lecture Notes in Physics Monographs 8
• Edition: 1
• Category: Library

✦ 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 theoreticalanalysis of convergence and the numerical implementation. Unlike other texts devoted to the subject this is a concise introduction that is ideally suited to the novice and practitioner alike, enabling them to assimilate themethods quickly and efficiently.

✦ Table of Contents

Front Matter....Pages I-X
Special Families of Polynomials....Pages 1-20
Orthogonality....Pages 21-34
Numerical Integration....Pages 35-63
Transforms....Pages 65-76
Functional Spaces....Pages 77-92
Results in Approximation Theory....Pages 93-124
Derivative Matrices....Pages 125-150
Eigenvalue Analysis....Pages 151-180
Ordinary Differential Equations....Pages 181-220
Time-Dependent Problems....Pages 221-248
Domain-Decomposition Methods....Pages 249-264
Examples....Pages 265-280
An Example in Two Dimensions....Pages 281-291
Back Matter....Pages 293-305

✦ Subjects

Mathematical Methods in Physics; Numerical and Computational Methods; Numerical Analysis