Browsing by Author "Uwaheren, O. A"
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Item Application of Adomian Decomposition Method on a Mathematical Model of malaria.(union of researchers of Macedonia., 2020) Abioye, A. I; Peter, O. J; Ayoade, A. A; Uwaheren, O. A; Ibrahim, M. OIn this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM’s efficiency and accuracy of ADM in finding the malaria model solution.Item Application of Homotopy Perturbation Method to an SIR Mumps Model(union of researchers of Macedonia., 2020) Ayoade, A. A; Peter, O. J; Abioye, A. I; Adinum, T. F; Uwaheren, O. AMumps is one of the diseases that pose global threat to children well-being. In this paper, the problem of the spread of mumps in a closed population is investigated using a SIR compartmental model. Mathematical interpretation of the problem generates nonlinear first-order differential equations. The method of Homotopy Perturbation is adopted to derive the theoretical solutions of the system. Numerical simulations of the analytical results are carried out with the help of Maple 18 software and the solutions are presented in graphical form. The solutions show that Homotopy Perturbation Method (HPM) is an appropriate technique for solving epidemic models.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 Exponentially Fitted Collocation Method for Solving Singular Multi-Fractional Integro-Differential Equations.(Published by Academic Staff Union of Universities., 2019) Owolanke, A. O; Taiwo, A. O; Uwaheren, O. AThis work considered the construction of canonical polynomials and used as basis functions for the approximation of singular multi-order fractional integro-differential equations. The idea is that the singular multi-order problem is slightly perturbed with shifted Chebyshev polynomials, and the resulting equation is collocated at equally spaced interior points. The conditions are exponentially fitted with one tau-parameter along with the unknown constants. This results into a system of linear algebraic equations which are then solved using Gaussian elimination method to obtain the unknown parameters involved. Some examples are solved to demonstrate the effectiveness of the method.Item Least Squares Bernstein Method for Solving Fractional Integro- Differential Equations(Faculty of Technology Education, Abubakar Tafawa Balewa University Bauchi., 2022) Oyedepo, T; Ishola, C. Y; Uwaheren, O. A; Olaosebikan, M. L; Ajisope, M. O; Victor, A. AThis study gears towards finding a simple numerical algorithm for the solution to fractional integro-differential equations. The technique involves the application of Caputo properties and the properties of Bernstein polynomials to reduce the problem to system of linear algebraic equations and then solved using MAPLE 18. To demonstrate the accuracy and applicability of the presented method some numerical examples are given. Numerical results show that the method is easy to implement and compares favorably with the exact results. The graphical solution of the method is displayedItem Least Squares Technique for Solving Volterra Fractional Integro-differential Equations Based on Constructed Orthogonal Polynomials(Akamai University, Hawaii, USA., 2020) Oyedepo, T; Adebisi, A. F; Uwaheren, O. A; Ishola, C. Y; Amadiegwum, S; Latunde, TIn this study, a new Gauss-Legendre Polynomials basis function was constructed and used for solving integro-differential difference equations using standard collocation method. An assumed approximate solution in terms of the constructed polynomial was substituted into the general class of integro-differential difference equation considered. The resulted equation was collocated at appropriate points within the interval of consideration to obtain a system of algebraic linear equations. Solving the system of equations, the unknown constant coefficients involved in the equations are obtained. The required approximate solution is obtained when the values of the constant coefficients are substituted back into the assumed approximate solution. Some numerical examples were solved to demonstrate the method.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 18Item Solution of Fractional Integro-differential Equation Using modified Homotopy Perturbation Technique and Construction orthogonal polynomials as Basis Functions(Faculty of Technology Education, Abubakar Tafawa Balewa University Bauchi., 2019) Oyedepo, T; Uwaheren, O. A; Okperhe, P; Peter, O. JA numerical methodology based on quartic weighted polynomials for finding the solution of fractional integro-differential equations (FIDEs) is presented. The fractional derivative is taken into account within in the Caputo sense. The suggested method involves the application of the homotopy perturbation method and used the initial approximation as the constructed orthogonal polynomials. The ensuing equations involve comparing the coefficients of the homotopy parameter P, which then resulted in a system of a linear algebraic equation and then solved using MAPLE 18. To demonstrate the relevance of the bestowed methodology some numerical examples were solved, and the numerical results obtained show that the techniques are easy to implement and accurate when applied to fractional FIDEs. The graphical solution of the method is displayed.Item Solution of an SIR Infectious Disease Model by Differential Transform Method.(ATBU Journal of Science, Technology and Education, 2021) Olaosebikan, M. L; Victor, A. A; Uwaheren, O. A; Ayoola, T. A; Ajisope, M. OA mathematical model on the transmission dynamics of infectious disease using the concept of differential equation was developed. Differential Transform Method (DTM) was employed to attempt the series solution of the model. The validity of the DTM in solving the model was established by classical fourth-order Runge-Kutta method implemented in Maple 18. The comparism between DTM solution and Runge- Kutta(RK4) were performed. The results obtained confirm the accuracy and potential of the DTM to cope with the analysis of modern epidemics.