This article is cited in 1 paper

Mathematical Modelling

Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels

A. Tynda^a, D. Sidorov^bc, I. Muftahov<sup>bd

a</sup> Penza State University, Penza, Russian Federation
^b Melentiev Energy Systems Institute SB RAS, Irkutsk, Russian Federation
^c Irkutsk National Research Technical University, Irkutsk, Russian Federation
^d Main Computing Center of JSC Russian Railways, Irkutsk, Russian Federation

Abstract: Volterra integral equations find their application in many areas, including mathematical physics, control theory, mechanics, electrical engineering, and in various industries. In particular, dynamic Volterra models with discontinuous kernels are effectively used in power engineering to determine the operating modes of energy storage devices, as well as to solve the problem of load balancing. This article proposes the numerical scheme for solution of the fractional order linear Volterra integral equations of the first kind with piecewise continuous kernels. The developed approach is based on a polynomial collocation method and effectively approximate such a weakly singular integrals. The efficiency of proposed numerical scheme is illustrated by two examples.

Keywords: Volterra integral equations, numerical method, convergence, discontinuous kernel, singularity, fractional integral.

UDC: 517.968.22

MSC: 45D05, 34A08, 65R20

Received: 05.10.2020

Language: English

DOI: 10.14529/mmp200405