Handbook of Sinc Numerical Methods

Frank Stenger

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December 2, 2010 by CRC Press
Handbook - 482 Pages - 56 B/W Illustrations
ISBN 9781439821589 - CAT# K11144
Series: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

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Features

  • Develops methods for solving linear and nonlinear PDE problems with emphasis on elliptic, hyperbolic, and parabolic PDEs
  • Applies MATLAB to a range of real-world problems
  • Covers many novel derivations, including Laplace transform inversion and indefinite convolution
  • Explores advances in nonlinear convolutions and analytic continuation
  • Offers new insights into properties of PDEs and IEs
  • Explains the unification of Sinc series and Fourier and algebraic polynomials
  • Provides a solution to Wiener–Hopf problems
  • Discusses the Sinc separation of variables method
  • Includes Sinc-Pack programs on an accompanying CD-ROM

Summary

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.