Browsing by Author "A. Abubakar"

Now showing 1 - 4 of 4
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    Exact Solution of Fractional Order Integro-Differential Equations by Collocation Method
    (Ibrahim Badamasi Babangida University, Lapai., 2018) K.A. Bello; O.A. Taiwo; F.A Adebisi; A. Abubakar
    In this paper, the application of standard collocation method on fractional integro-differential equation was carried out by assuming a modified trial solution with chebyshev polynomial basis. Equally spaced interior collocation points was adopted. In built maple 18 was used for the computation of the four illustrative examples, for the simple demonstration of the applicability, validity and reliability of the method. It is however concluded that the method is considered as one of the novel solvers of the class of fractional integro-differential equation.
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    Extension of Picard’s Successful Iteration Method to Numerical Solution of Second Order Initial Value Problem
    (Faculty of Natural Sciences, Ibrahim Badamasi Babangida University, Lapai, Niger State, Nigeria, 2020) K.A. Bello; O.A. Taiwo; A. Abubakar
    In this paper, Picard’s successive iteration method, to obtain the numerical solution for second order initial value problem is derived. The derivation of the new method is purely based on differentiation of the general class of the problem, following the Picard’s first order iteration method steps with little modification and adjustment. The derived method is implemented on three numerical examples, and the result obtained converge positively to the exact solution as contained in literature.
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    On The Performance Of Four Kinds of Chebyshev Polynomial in Numerical Treatment of Multi-Order Fractional Differential Equations.
    (Ibrahim Badamasi Babangida University, Lapai, Niger State, 2019) Bello, K.A; Taiwo, O.A; Odetunde, O.A; A. Abubakar
    This paper is devoted to investigate the relationship in the performance of the four kinds of shifted Chebyshev polynomial for the comparison purpose, in fractional linear differential equation with constant co-efficient involving the Caputo fractional derivative, using Standard Collocation Method (SCM). Three different examples were considered and the results obtained show that the first kind of shifted Chebyshev polynomial performed better. Hence the order of performance is as follows: the first, fourth, second and third respectively.
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    Standard Collocation and Perturbed Collocation Methods for Solving Linear Volterra Integro Differential Equations
    (Ibrahim Badamasi Babangida University, Lapai., 2021) Bello, K.A; Taiwo, O.A; A. Abubakar; AdbdulKareem, A; M.A. Adeyanju; Ige, S.K.
    This project deals with the numerical approximation of linear fourth order integro differentia equations. The numerical methods consider are standard collocation and perturbed collocatio methods using shifted chebyshev polynomial as basis function. The result obtained shows tha perturbed collocation method proved to have a better approximation than that of standarc collocation methods in the cases considered. Three examples are considered to illustrat efficiency method.