Browsing by Author "Yisa, Babatunde Morufu"

Now showing 1 - 13 of 13
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    Analytical Approximate Solution of Nonlinear Initial Value Problems by Variational Iteration Method and Adomian Decomposition Method
    (Federal University of Technology, Minna, Nigeria., 2018-06-01) Yisa, Babatunde Morufu
    In this paper, variational iteration method and Adomian decomposity methodare applied to certain initial value problems with varied nonlinearities. The two methods are equally applied to linear problems just to demonstrate their effectiveness in handling such category of problems too. The two methods give identical results which closely estimate the exact solution whenever such exists, in all cases, for both linear and nonlinear problems.
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    Analytical Solutions of Nonlinear Initial-Boundary Value Problems
    (University of Ilorin, 2026-04-01) Yisa, Babatunde Morufu; Tijani, Saadatu Abubakar
    This work presents solutions to initial-boundary value problems that are generally nonlinearexploringTaylor’s theorem in a decomposition technic. Not until few decades back, real world phenomena in many fields of human endeavours were modelled into initial and boundary value problems. Due to identified deficiencies in doing that, initial-boundary value equations are used to achieve the aim.The problems are mostly nonlinear. Solution to such category of problems mostly defies the use of the established analytical methods. Most researchers employ numerical approaches that result in approximate solutions. The present approach uses Taylor’s theorem alongside Adomian decomposition method. The nonlinear aspect is treated by decomposing it into polynomials, while the resulting unknown terms are evaluated through Taylor’s expansion. The method is applied to eight problems in literature, all of which give exact solution. Mathematica 13.3 is employed for the simulations.
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    Comparative Analysis of the Numerical Effectiveness of the Four Kinds of Chebyshev Polynomials
    (Nigerian Association of Mathematical Physics, 2015-11-01) Yisa, Babatunde Morufu
    In this paper, four kinds of Chebyshev polynomials are studied with the aim of identifying which of them gives more reliable results. It was eventually discovered, based on numerical results, that the first and fourth kinds perform better than the second and third kinds. While further comparison revealed that the second kind did better than the third kind.
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    Mahgoub Homotopy Analysis Method for the Solutions of Nonlinear Ordinary and Partial Differential Equations
    (University of Ilorin, Nigeria., 2026-03-10) Yisa, Babatunde Morufu; Alade, Yusuf Aduragba
    Solving nonlinear problems involving both partial and ordinary differential equations is always more involving and mostly impossible through the well-established traditional analytical methods. We therefore proposed an analytical method that is derived through exploiting Mahgoub transform that is capable of solving variable coefficient linear differential equations. But this transform being unable to solve nonlinear problem, informed the integration of Homotopy analysis method to handle the nonlinear part. Thus, Mahgoub Homotopy Analysis Method (MHAM) that is proposed reduces the volume of computation as well as producing the exact solution of the problem considered. Mahgoub of all the terms in the given equation is taken, and most importantly the differential coefficient. The Mahgoub terms independent of nonlinear term constitute the initial approximation, while the recurrence relation is developed by using the nonlinear terms. The two important deformation equations in the HAM are therefore obtained. The final solution is arrived at via taking the inverse Mahgoub of terms. Few questions on both ordinary and partial differential equations are used to validate the proposed method. The coding and general computations are carried out via Mathematica 13.3.
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    Modified Results in Adaptive Quadrature Method for the Approximations of Integrals
    (Federal University, Lokoja, 2017-11-01) Yisa, Babatunde Morufu; Ahmed, Bayo Musa
    This paper investigates the role of higher order Newton – Cotes closed quadrature formula in the adaptive quadrature method for approximating integrals. Boole’s rule was specifically adopted as a result of its exceptional accuracy, and this was brought to bear in the numerical experiments that followed the derivation of error estimation scheme. The error estimate scheme facilitates the suitability of the method reported in this paper for situations where exact solution is extremely difficult to arrive at.
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    Numerical Approximation of space Fractional Order Wave Equation Using Shifted Chebyshev Polynomials of Second and third Kinds.
    (Nigerian Society for Mathematical Biology, University of Benin, Benin City, 2023-10-01) Yisa, Babatunde Morufu; Oyetunji, Mayowa Elijah; Olotu, Thomas O.
    In this paper,we proposed a numerical method to solve space fractional order wave equation (SFOWE). The method implements shifted Chebyshev polynomials of the second and third kinds with the fractional derivative interpreted in Caputo sense. Chebyshev collocation method is adopted to reduce the problem to a system of second order ordinary differential equation, while the finite difference method reduces that to a system of linear algebraic equations. The system of algebraic equations thus formed is solved with the aid of Mathematica 11.0. The proposed method gives results that compared favourably with existing results in the literature, while it is observed that the performance of second kind is relatively superior to that of the third kind polynomials. The results are presented in both tabular and 3D graphs, for ease of comparison.
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    Numerical Performances of Two Orthogonal Polynomials in the Tau Method for Solutions of Ordinary Differential Equations
    (Nigerian Association of Mathematical Physics, 2015-05-01) Yisa, Babatunde Morufu
    In this work, efforts are made at comparing the numerical effectiveness of two most accurate orthogonal polynomials; Chebyshev and Legendre polynomials. Although the two have different weight functions, but they most time give close results especially when they are considered in the same interval. This work has therefore used the two polynomials, withing the same interval, as bases functions in the Ortiz’s Recursive Formulation of Lanczos’s Tau method. Numerical experiments show that the two are very accurate.
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    Numerical Solutions of Fredholm Integral Equations of the Second Kind Using Certain Quadratures
    (Federal University of Technology, Minna, Nigeria., 2016-12-01) Yisa, Babatunde Morufu; Aderinto, Yidiat O.
    In this paper, nonhomogeneous Fredholm integral equations of the second kind are approximated using Boole’s and Weddle’s rules. The kernels of the family of integral equations are approximated by the two quadrature formulae due to their accuracy. In most of the problems solved, the two quadratures give exact solutions, but where the exact solution is not obtained, the numerical approximation realized are very reasonable.
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    On Subgroups of Non-Commutative Orthogonal Rhotrix Group
    (Published by Al-Hikmah University, Ilorin, Nigeria., 2026-04-14) Ahmed, Bayo Musa; Yisa, Babatunde Morufu; Ayinla, Yeketi A.
    This study investigates the algebraic structure of the noncommutative orthogonal rhotrix group under rhotrix row-column multiplication. The special orthogonal, diagonal orthogonal, and special diagonal orthogonal rhotrix groups are identified as subgroups, and their internal relationships are explicitly characterized through subgroup inclusions and intersections. In particular, it is shown that the orthogonal rhotrix group embeds as a subgroup of the general linear rhotrix group. To the best of our knowledge, this work provides the first systematic subgroup structural analysis of non-commutative orthogonal rhotrix groups. These results clarify the internal organization of orthogonal rhotrix groups and provide a foundational framework for further studies on normal subgroups, quotient structures, and related non-commutative rhotrix construction.
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    On the Variants of the Tau Methods for Solutions of IVPs in Systems of First Order Differential Equations
    (Kwara State Mathematical Association of Nigeria, 2010-03-01) Yisa, Babatunde Morufu; Adeniyi, Raphael Babatunde
    This paper is concerned with two variants of a numerical integration scheme, namely, the tau method for systems of first order ordinary differential equations. The error estimation of the two variants are obtained and numerical results confirm the accuracy and effectiveness of the scheme.
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    Relative in Numerical Performance of Certain Polynomials in Tau Method
    (Federal University of Technology, Minna, Nigeria., 2015-12-01) Yisa, Babatunde Morufu
    This paper examines the order of numerical usefulness of the four kinds of Chebyshev polynomials, especially in the differential formulation of the Lanczos’ Tau method. Their practical applications on selected numerical problems, which are constant and variable coefficients, homogeneous and nonhomogeneous problems of varied orders, showed correlation between the accuracy first and fourth kinds. The second kind was next in performance, while the third kind performed least.
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    Solution of Ordinary Differential Equations with Special Nonlinearities by Adomian Decomposition Method
    (Federal University of Technology, Minna, Journal of Science, Technology, Mathematics and Education (JOSTMED), 2019-09-01) Yisa, Babatunde Morufu
    In this paper, the generation of Adomian polynomials for certain supposedly difficult nonlinearities and their implementation in standard Adomian decomposition method is reported. The steps involved in the whole process are well elucidated, and the numerical results obtained confirm the accuracy of the method.
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    Solutions of Fractional Order Integro-differential Equations by Two Semi-analytical Methods.
    (Nigerian Society for Mathematical Biology, University of Benin, Benin City., 2023-10-01) Yisa, Babatunde Morufu; Yusuf, Zainab Bukola
    This paper is concerned with the solution of fractional order integro-differential equations where the fraction order, 𝜂 is in the interval (3, 4]. Two semi-analytical methods; Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) are implemented for the solution of the class of problems considered. Few examples are solved and the results obtained compared favorably with the existing results in the literature. All codes used in solving the problems are written in Mathematica 11.3