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 CD-ROM of this handbook contains roughly 450 MATLAB(R) 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 QuadraturesSinc Methods on Î Rational Approximation at Sinc PointsPolynomial Methods at Sinc Points Sinc Convolution-BIE Methods for PDE and IE Introduction and Summary Some Properties of Green's FunctionsFree-Space Green's Functions for PDELaplace Transforms of Green's FunctionsMulti-Dimensional Convolution Based on SincTheory of Separation of Variables Explicit 1-d Program Solutions via Sinc-PackIntroduction and Summary Sinc InterpolationApproximation of Derivatives Sinc Quadrature Sinc Indefinite Integration Sinc Indefinite Convolution Laplace Transform Inversion Hilbert and Cauchy Transforms Sinc Solution of ODEWavelet Examples Explicit Program Solutions of PDE via Sinc-Pack Introduction and Summary Elliptic PDEHyperbolic PDEParabolic PDE Performance Comparisons Directory of Programs Wavelet Formulas One Dimensional Sinc ProgramsMulti-Dimensional Laplace Transform Programs Bibliography Index
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.
Reviews for Handbook of Sinc Numerical Methods
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