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Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering

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Transcendental Bernstein Series: Interpolation and Approximation

Author(s): Z. Avazzadeh, H. Hassani*, J.A. Tenreiro Machado, P. Agarwal and E. Naraghirad

Pp: 73-93 (21)

DOI: 10.2174/9789815079333123010007

* (Excluding Mailing and Handling)

Abstract

This paper adopts the transcendental Bernstein series (TBS), a set of basis functions based on the Bernstein polynomials (BP), for approximating analytical functions. The TBS is more accurate than the BP method, particularly in approximating functions including one or more transcendental terms. The numerical results reveal also the applicability and higher computational efficiency of the new approach.

Keywords: Transcendental functions; Bernstein polynomials; Transcendental Bernstein series.

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