NUMERICAL SOLUTION OF DISTRIBUTED ORDER INTEGRO-DIFFERENTIAL EQUATIONS

Anqi Zhang, Roghayeh Moallem Ganji, Hossein Jafari, Mahluli Naisbitt Ncube and Latifa Agamalieva
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Anqi Zhang: School of Management, Shanghai University of International Business and Economics, Shanghai, P. R. China
Roghayeh Moallem Ganji: ��Department of Mathematics, University of Mazandaran, Babolsar, Iran
Hossein Jafari: ��Department of Mathematics, University of Mazandaran, Babolsar, Iran‡Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa§Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan¶Science Department, Azerbaijan University, Jeyhun Hajibeyli Str. 71, AZ1007 Baku, Azerbaijan
Mahluli Naisbitt Ncube: ��Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa
Latifa Agamalieva: �Science Department, Azerbaijan University, Jeyhun Hajibeyli Str. 71, AZ1007 Baku, Azerbaijan∥Institute for Physical Problems, Baku State University, Z. Khalilov Str. 23, AZ1148 Baku, Azerbaijan

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-11

Abstract: In this paper, a numerical algorithm is presented to obtain approximate solution of distributed order integro-differential equations. The approximate solution is expressed in the form of a polynomial with unknown coefficients and in place of differential and integral operators, we make use of matrices that we deduce from the shifted Legendre polynomials. To compute the numerical values of the polynomial coefficients, we set up a system of equations that tallies with the number of unknowns, we achieve this goal through the Legendre–Gauss quadrature formula and the collocation technique. The theoretical aspects of the error bound are discussed. Illustrative examples are included to demonstrate the validity and applicability of the method.

Keywords: Distributed Order Integro-Differential Equations; Operational Matrix; The Legendre–Gauss Quadrature; Volterra–Fredholm Integro-Differential Equations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401235

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