Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
Abstract
In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative is given in Caputo's sense. The operational matrices of the second kind Chebyshev polynomials reduce the given equations to a system of linear algebraic equations. An approximate solution is calculated by extending the functions in terms of the second kind Chebyshev polynomials and applying operational matrices. Unknown coefficients are obtained by solving the final system of linear equations. Also, convergence analysis and error bound of the solution are studied in this paper. Moreover, to check the reliability and accuracy of the given method. The numerical examples have been shown and the results of the described method are compared with the Haar wavelet method. The obtained results authenticate that the displayed method is effortless to analyze and perform such types of problems. All methods for the proposed method are applied in MATLAB (R2020b) software.
Derakhshan,M. H. (2021). Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials. Mathematical Analysis and its Contemporary Applications, 3(4), 25-40. doi: 10.30495/maca.2021.1938222.1025
MLA
Derakhshan,M. H. . "Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials", Mathematical Analysis and its Contemporary Applications, 3, 4, 2021, 25-40. doi: 10.30495/maca.2021.1938222.1025
HARVARD
Derakhshan M. H. (2021). 'Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials', Mathematical Analysis and its Contemporary Applications, 3(4), pp. 25-40. doi: 10.30495/maca.2021.1938222.1025
CHICAGO
M. H. Derakhshan, "Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials," Mathematical Analysis and its Contemporary Applications, 3 4 (2021): 25-40, doi: 10.30495/maca.2021.1938222.1025
VANCOUVER
Derakhshan M. H. Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials. MACA, 2021; 3(4): 25-40. doi: 10.30495/maca.2021.1938222.1025
