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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.

MSC:

65D15 Algorithms for approximation of functions
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
65T40 Numerical methods for trigonometric approximation and interpolation
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