Browsing by Author "Taiwo, O. A"
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Item A Collocation Technique based on an Orthogonal Polynomial for Solving Malti-Order Fractional Integro-differential Equations.(Mathematical Association of Nigeria, 2016-09-30) Uwaheren, O. A; Taiwo, O. AThis paper deals with construction of orthogonal polynomial functions and the application of same to solve multi-order fractional integro – differential equations. The method used in the equation is referred to as the standard collation method. The method assumes an approximate solution in which the constructed orthogonal polynomials are used as basis functions. The assumed solution is substituted into the general class of multi- order fractional integro- differential equations and the resulting equation is then collocated at equally spaced interior points, thus resulting in algebraic linear system of equations which are to be solved by Gaussian elimination method in order to obtain the unknown constants in the assumed solution. Some numerical examples are presented to illustrate the validity and applicability of the method. The results obtained using the method is shown on tables of results.Item Computational methods for higher order linear and non linear integro differential equations by collocation(Mathematical Association of Nigeria, 2017-09-29) Gegele, O. A; Taiwo, O. A; Uwaheren, O. A; Etuk, M. OIn this paper, we present two spline collocation methods namely standard cubic spline and non- polynomial spline collocation to solve third and fourth order linear and non-linear integro differential equations. Newton Kantorovich scheme was used to linearize the non-linear term in the case of non- linear equation and this leads to an iterative procedure. The resulting system of linear algebraic equations are the solved using Maple 13. The methods are applied to few examples to illustrate the accuracy and effectiveness of the methods.Item EXACT SOLUTION OF FRACTIONAL ORDER INTEGRO-DIFFERENTIAL EQUATIONS BY COLLOCATION METHOD(2018) Bello, K. A.; Taiwo, O. A; Abubakar, A.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 collacation 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 solver of the class of fractional integro-differential equation.Item Multiple Perturbed Collocation Tau-method for Solving High Order Linear and Non-Linear Boundary Value Problems(2014) Adebisi, A. F.; Taiwo, O. A; Adewumi, A.O; Bello, K. A.This paper is concerned with the numerical solution of high order linear and nonlinear boundary value problems of ordinary differential equations by Multiple Perturbed Collocation Tau Method (MPCTM). We assumed a perturbed apporoximate solution in terms of Chebyshev polynomial basis function which is subtituted into the special class of the problem considered. Thus, resulting into n-folds integration. After evaluation of n-fold integration, the resulting equation is then collocation at equally spaced interior points and the unknown constants in the approximate solution are then obtained by Gaussian elimination method which are then substituted back into the approximate solution. The proposed method is tested on several numerical examples, the approximate solution is in agreement with the exact solution. The approximate results obtained by the proposed method confirm the convergency of numerical solutions and are compared favourably with the existing methods available in literature.Item Numerical solution of multi-order fractional differential equations using orthogonal polynomial basis(Mathematical Association of Nigeria, 2017-09-29) Uwaheren, O. A; Taiwo, O. AThis paper presents the solution of multi-order fractional differential equations using a constructed orthogonal polynomial as the basis function. An approximate solution was assumed and substituted into a general class of multi-order fractional differential equations of the form Dα1y(x)+Dα2y(x)+⋯+Dαny(x)=f(x) With initial conditions y(0)=μ Where Dα are parameters denoting the fractional order derivatives in Caputo sense. The resulting equation was collocated equally spaced interior points. The unknown constants in the assumed approximate solution were obtained using Gaussian elimination method. Some numerical examples are presented to illustrate the methodItem Perturbed Collocation Method for Solving Singular Multi-order Fractional Differential Equations of Lame-Emden Type(Journal of the Nigerian Society of Physical Sciences, 2020) Uwaheren, O. A; Adebisi, A. F; Taiwo, O. AIn this work, a general class of multi-order fractional di erential equations of Lane-Emden type is considered. Here, an assumed approximate solution is substituted into a slightly perturbed form of the general class and the resulting equation is collocated at equally spaced interior points to give a system of linear algebraic equations which are then solved by suitable computer software; Maple 18