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    A two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations
    (2022-12-31) AbdulAzeez Kayode Jimoh; Adebayo Olusegun Adewumi
    A continuous two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations is proposed. The approximate solution in form of power series and its first ordered derivative are respectively interpolated at the point x = 0 and collocated at equally spaced points in the interval of consideration. The application of the method involves using the main scheme derived together with the additional schemes simultaneously to obtain the solution to the problem at the grid points. The analysis of the method and the results obtained from the examples considered show that the method is consistent, zero-stable, convergent and of high accuracy.
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    Approximate solution of space fractional order diffusion equations by Gegenbauer collocation and compact finite difference scheme
    (Nigerian Society of Physical Sciences, 2023-05-22) Kazeem Issa; Steven Ademola Olorunnisola; Tajudeen Aliu; Adeshola Adeniran Dauda
    In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N - 1) degree shifted Gegenbauer polynomial as collocation points. The important feature in this approach is that it reduces the problems to algebraic linear system of equations together with the boundary conditions gives (N + 1) linear equations. Some theorems are given to establish the convergence and the stability of the proposed method. To validate the efficiency and the accuracy of the method, obtained results are compared with the existing results in the literature. The graphical representation are also displayed for various values of \beta Gegenbauer polynomials. It can be observe in the tables of the results and figures that the proposed method performs better than the existing one in the literature.
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    Approximate Solution of Perturbed Volterra-Fredholm Integrodifferential Equations by Chebyshev-Galerkin Method
    (Hindawi, 2017-01-12) K. Issa; F. Salehi
    In this work, we obtain the approximate solution for the integrodifferential equations by adding perturbation terms to the right hand side of integrodifferential equation and then solve the resulting equation using Chebyshev-Galerkin method. Details of the method are presented and some numerical results along with absolute errors are given to clarify the method. Where necessary, we made comparison with the results obtained previously in the literature. The results obtained reveal the accuracy of the method presented in this study.
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    Comparison of some numerical methods for the solution of fourth order integro-differential equations
    (2014-11) A. K. Jimoh; K. Issa
    The numerical methods for solving fourth order integro-differential equations are presented. The methods are based on replacement of the unknown function by power series and Legendre polynomials of appropriate degree. The proposed methods convert the resulting equation by some examples considered show that the standard collocation method proved superior to the perturbed collocation method. Two examples are considered to illustrate the efficiency and accuracy of the methods.
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    An error estimation of a numerical scheme analogue to the tau method for initial value problems in ordinary differential equations
    (2014-03) K. ISSA; A. K. JIMOH
    In a recent paper, we constructed three classes of orthogonal polynomials for use in the perturbation term of a numerical integration scheme analogues to the tau method of Lanczos and Ortiz for ordinary differential equations. The resulting n-th degree approximant y_n(x) of the solution y(x) of the differential equation was accurate and hence justified the scheme. In this present paper, we report an error estimation of the method based on our earlier work. The estimate obtained is good as it correctly captured the order of the tau approximant.