NUMERICAL ANALYSIS of FRACTIONAL ORDER INTEGRAL DYNAMICAL MODELS with PIECEWISE CONTINUOUS KERNELS

A. Tynda; D. Sidorov; I. Muftahov

doi:10.14529/mmp200405

NUMERICAL ANALYSIS of FRACTIONAL ORDER INTEGRAL DYNAMICAL MODELS with PIECEWISE CONTINUOUS KERNELS

A. Tynda
, D. Sidorov
, I. Muftahov

Penza State University
Melent'ev Institute of Power Engineering Systems
Irkutsk National Research Technical University
Irkutsk Department

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	58-65
Number of pages	8
Journal	Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software
Volume	13
Issue number	4
DOIs	https://doi.org/10.14529/mmp200405
State	Published - Nov 2020
Externally published	Yes

Keywords

Convergence
Discontinuous kernel
Fractional integral
Numerical method
Singularity
Volterra integral equations

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10.14529/mmp200405

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title = "NUMERICAL ANALYSIS of FRACTIONAL ORDER INTEGRAL DYNAMICAL MODELS with PIECEWISE CONTINUOUS KERNELS",

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 = "Convergence, Discontinuous kernel, Fractional integral, Numerical method, Singularity, Volterra integral equations",

author = "A. Tynda and D. Sidorov and I. Muftahov",

year = "2020",

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doi = "10.14529/mmp200405",

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T1 - NUMERICAL ANALYSIS of FRACTIONAL ORDER INTEGRAL DYNAMICAL MODELS with PIECEWISE CONTINUOUS KERNELS

AU - Tynda, A.

AU - Sidorov, D.

AU - Muftahov, I.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Convergence

KW - Discontinuous kernel

KW - Fractional integral

KW - Numerical method

KW - Singularity

KW - Volterra integral equations

UR - https://www.scopus.com/pages/publications/85099652802

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DO - 10.14529/mmp200405

M3 - 文章

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SN - 2071-0216

VL - 13

SP - 58

EP - 65

JO - Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software

JF - Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software

IS - 4

ER -

NUMERICAL ANALYSIS of FRACTIONAL ORDER INTEGRAL DYNAMICAL MODELS with PIECEWISE CONTINUOUS KERNELS

Abstract

Keywords

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