Application of Steklov's method of smoothing functions to numerical differentiation and construction of local quasi-interpolation splines

T. Zhanlav^a, Yu. S. Volkov^b, R.-O. Mijiddorj<sup>c

a</sup> Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia
^b Sobolev Institute of Mathematics, Siberian Branch Russian Academy of Sciences, Novosibirsk, Russia
^c Mongolian National University of Education, Ulaanbaatar, Mongolia

Abstract: We mainly aim to utilize the Steklov smoothing method to approximate a function and its derivatives. Subsequently, we can readily construct integro splines in the case of a uniform grid. It has been demonstrated that the Steklov smoothing method is highly effective for achieving this purpose. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Key words: smoothing Steklov function, integro spline, quasi-interpolating spline.

UDC: 519.65

Received: 04.02.2025
Revised: 23.04.2024
Accepted: 11.06.2025

DOI: 10.25205/1560-750X-2025-28-2-28-49