1st Edition

Handbook of Sinc Numerical Methods

By Frank Stenger Copyright 2011
    482 Pages 56 B/W Illustrations
    by CRC Press

    484 Pages 56 B/W Illustrations
    by CRC Press

    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.

    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




    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