Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations

In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To ca...

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Bibliographic Details
Published in:Advances in difference equations 2021-10, Vol.2021 (1), p.435-14, Article 435
Main Authors: Jafari, H., Nemati, S., Ganji, R. M.
Format: Article
Language:English
Subjects:
Analysis
Applied mathematics
Calculus
Chebyshev approximation
Convergence analysis
Coronaviruses
Difference and Functional Equations
Differential equations
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear integro-differential equations
Operational matrix
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Shifted fifth-kind Chebyshev polynomials
Variable order
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Summary:In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the operational matrices depending on the SFKCPs to find an approximate solution of the original problem. These matrices, together with the collocation points, are used to transform the original problem to form a system of linear or nonlinear algebraic equations. We discuss the convergence of the method and then give an estimation of the error. We end by solving numerical tests, which show the high accuracy of our results.
ISSN:1687-1839
1687-1847
1687-1847
DOI:10.1186/s13662-021-03588-2