Handbook of Sinc Numerical Methods

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® 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.

Frank Stenger is a professor emeritus at theUniversity 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.

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 ΓRational 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