Mathematics and Statistics Vol. 10(2), pp. 378 - 382
DOI: 10.13189/ms.2022.100212
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Fractional Variational Orthogonal Collocation Method for the Solution of Fractional Fredholm Integro-Differential Equation Using Mamadu-Njoseh Polynomials

Jonathan Tsetimi ^*, Ebimene James Mamadu
Department of Mathematics, Delta State University, Abraka, Nigeria

ABSTRACT

The use of orthogonal polynomials as basis functions via a suitable approximation scheme for the solution of many problems in science and technology has been on the increase and quite fascinating. In many numerical schemes, the convergence depends solely on the nature of the basis function adopted. The Mamadu-Njoseh polynomials are orthogonal polynomials developed in 2016 with reference to the weight function, which bears the same convergence rate as that of Chebyshev polynomials. Thus, in this paper, the fractional variational orthogonal collocation method (FVOCM) is proposed for the solution of fractional Fredholm integro-differential equation using Mamadu-Njoseh polynomials (MNP) as basis functions. Here, the proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). The VIM is one of the popular methods available to researchers in seeking the solution to both linear and nonlinear differential problems requiring neither linearization nor perturbation to arrive at the required solution. Collocating at the roots of orthogonal polynomials gives birth to the OCM. For the proposed method, the VIM is initiated to generate the required approximations whereby producing the series which is collocated orthogonally to derive the unknown parameters. The numerical results show that the method derives a high accurate and reliable approximation with a high convergence rate. We have also presented the existence and uniqueness of solution of the method. All computational frameworks in this research are performed via MAPLE 18 software.

KEYWORDS
Orthogonal Collocation, Mamadu-Njoseh Polynomials, Fredholm Integro-Differential Equations, Fractional Derivatives, Variational Iteration Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Jonathan Tsetimi , Ebimene James Mamadu , "Fractional Variational Orthogonal Collocation Method for the Solution of Fractional Fredholm Integro-Differential Equation Using Mamadu-Njoseh Polynomials," Mathematics and Statistics, Vol. 10, No. 2, pp. 378 - 382, 2022. DOI: 10.13189/ms.2022.100212.

(b). APA Format:
Jonathan Tsetimi , Ebimene James Mamadu (2022). Fractional Variational Orthogonal Collocation Method for the Solution of Fractional Fredholm Integro-Differential Equation Using Mamadu-Njoseh Polynomials. Mathematics and Statistics, 10(2), 378 - 382. DOI: 10.13189/ms.2022.100212.