Handbook of Sinc Numerical Methods  book cover
1st Edition

Handbook of Sinc Numerical Methods

ISBN 9781138116177
Published May 31, 2017 by CRC Press
482 Pages 56 B/W Illustrations

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Book Description

Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author’s advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to scientists and engineers. This new theory, which combines Sinc convolution with the boundary integral equation (IE) approach, makes for exponentially faster convergence to solutions of differential equations. The basis for the approach is the Sinc method of approximating almost every type of operation stemming from calculus via easily computed matrices of very low dimension.

The downloadable resources of this handbook contain roughly 450 MATLAB® programs corresponding to exponentially convergent numerical algorithms for solving nearly every computational problem of science and engineering. While the book makes Sinc methods accessible to users wanting to bypass the complete theory, it also offers sufficient theoretical details for readers who do want a full working understanding of this exciting area of numerical analysis.

Table of Contents

One-Dimensional Sinc Theory
Introduction and Summary
Sampling over the Real Line
More General Sinc Approximation on R
Sinc, Wavelets, Trigonometric and Algebraic Polynomials and Quadratures
Sinc Methods on Γ
Rational Approximation at Sinc Points
Polynomial Methods at Sinc Points

Sinc Convolution-BIE Methods for PDE and IE
Introduction and Summary
Some Properties of Green’s Functions
Free-Space Green’s Functions for PDE
Laplace Transforms of Green’s Functions
Multi-Dimensional Convolution Based on Sinc
Theory of Separation of Variables

Explicit 1-d Program Solutions via Sinc-Pack
Introduction and Summary
Sinc Interpolation
Approximation of Derivatives
Sinc Quadrature
Sinc Indefinite Integration
Sinc Indefinite Convolution
Laplace Transform Inversion
Hilbert and Cauchy Transforms
Sinc Solution of ODE
Wavelet Examples

Explicit Program Solutions of PDE via Sinc-Pack
Introduction and Summary
Elliptic PDE
Hyperbolic PDE
Parabolic PDE
Performance Comparisons

Directory of Programs
Wavelet Formulas
One Dimensional Sinc Programs
Multi-Dimensional Laplace Transform Programs



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Frank Stenger is a professor emeritus at the University of Utah, where he received the distinguished research award. One of the leading contributors to the area of numerical analysis, Dr. Stenger is the main developer of Sinc numerical methods and has authored over 160 papers in various journals.


The author, a well-known expert in this area, has published many papers dealing with various aspects of sinc methods. A key result is that sinc methods can converge very fast under certain assumptions on the given problem. … practical aspects are covered in great detail. In particular, there is an accompanying CD-ROM that contains about 450 MATLAB programs where sinc methods are implemented to solve various problems. The book provides a good description of these programs, so a user with a certain equation to solve can easily find an appropriate sinc algorithm. … it should be useful reading for practitioners who have heard about sinc methods and want to use them.
—Kai Diethelm, Computing Reviews, September 2011