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Summary of Sinc numerical methods. (English) Zbl 0964.65010

This article attempts to summarize the existing numerical methods based on Sinc approximation. Starting with a comparison of polynomial and Sinc approximation, basic formulas for the latter in the one-dimensional case are given. The author also covers the following:

(i) Explicit spaces of analytic functions for one dimensional Sinc approximation,

(ii) applications of Sinc indefinite integration and collocation to the solution of ordinary differential equation initial and boundary value problems,

(iii) results obtained for solution of partial differential equations, via Sinc approximation of the derivatives,

(iv) some results obtained on the solutions of integral equations,

(v) use of Sinc convolution, a technique for evaluating one and multi-dimensional convolution-type integrals.

A list of some existing computer algorithms based on Sinc methods is also given.

65D15Algorithms for functional approximation
65-02Research monographs (numerical analysis)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65M70Spectral, collocation and related methods (IVP of PDE)
65N35Spectral, collocation and related methods (BVP of PDE)
65R20Integral equations (numerical methods)
65T40Trigonometric approximation and interpolation (numerical methods)