A New First Finite Class of Classical Orthogonal Polynomials Operational Matrices: An Application for Solving Fractional Differential Equations

Authors

DOI:

https://doi.org/10.37256/cm.4420232716

Keywords:

tau method, collocation method, fractional-order differential equations, operational matrix, classical orthogonal polynomials, error bounds for initial value, initial boundary value problems

Abstract

In this paper, new operational matrices (OMs) of ordinary and fractional derivatives (FDs) of a first finite class of classical orthogonal polynomials (FFCOP) are introduced. Also, two algorithms are proposed for using the tau and collocation spectral methods (SPMs) to get new approximate solutions to the given fractional differential equations (FDEs). These algorithms convert the given FDEs subject to initial/boundary conditions (I/BCs) into linear or nonlinear systems of algebraic equations that can be solved using appropriate solvers. To demonstrate the robustness, efficiency, and accuracy of the proposed spectral solutions, several illustrative examples are presented. The obtained results show that the proposed algorithms exhibit higher accuracy compared to existing techniques in the literature. Furthermore, an error analysis is provided.

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Published

2023-11-10

How to Cite

1.
Ahmed HM. A New First Finite Class of Classical Orthogonal Polynomials Operational Matrices: An Application for Solving Fractional Differential Equations. Contemp. Math. [Internet]. 2023 Nov. 10 [cited 2024 Oct. 11];4(4):974-9. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2716