A.-R. K. Ramazanov, A. K. Ramazanov, V. G. Magomedova, “On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions”, Mat. Zametki, 2022, Volume 111, Issue 4,Pages <nobr>581

This article is cited in 2 papers

On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions

A.-R. K. Ramazanov^ab, A. K. Ramazanov^c, V. G. Magomedova^a

^a Daghestan State University, Makhachkala
^b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
^c Kaluga Branch of Bauman Moscow State Technical University

Abstract: The approximate solution of the Volterra integral equation of the second kind is represented as collocation rational spline functions on successive closed intervals exhausting the entire solution domain. Estimates for the rate of convergence of approximate solutions to the exact solution in the uniform metric are also obtained via the modulus of continuity of the solution and its derivatives of first and second order.

Keywords: rational spline functions, Volterra equation, collocation method.

UDC: 519.64+519.65

Received: 23.09.2021
Revised: 23.11.2021

DOI: 10.4213/mzm13303