Browsing by Author "Kazeem Issa"

Now showing 1 - 8 of 8
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    An algorithm for choosing best shape parameter for numerical solution of partial differential equation via inverse multiquadric radial basis function
    (2020-04-30) Kazeem Issa; Sulaiman M. Hambali; Jafar Biazar
    Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
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    Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial
    (Nigerian Society of Physical Sciences, 2024-12-21) Kazeem Issa; Risikat A. Bello; Usman Jos Abubakar
    In this paper, we extend fractional-order derivative for the shifted Vieta-Lucas polynomial to generalized-fractional integro-differential equations involving non-local boundary conditions using Galerkin method as transformation technique and obtained N - \delta + 1 system of linear algebraic equations with \lambda i, i = 0, . . . , N unknowns, together with \delta non-local boundary conditions, we obtained (N + 1)- linear equations. The accuracy and effectiveness of the scheme was tested on some selected problems from the literature. Judging from the table of results and figures, we observed that the approximate solution corresponding to the problem that has exact solution in polynomial form gives a closed form solution while problem with non-polynomial exact solution gives better accuracy compared to the existing results.
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    Approximate analytical solution of fractional-order generalized integro-differential equations via fractional derivative of shifted Vieta-Lucas polynomial
    (2024) Kazeem Issa; Risikat A. Bello; Usman Jos Abubakar
    In this paper, we extend fractional-order derivative for the shifted Vieta-Lucas polynomial to generalized-fractional integro-differential equations involving non-local boundary conditions using Galerkin method as transformation technique and obtained N - \delta + 1 system of linear algebraic equations with \lambda i, i = 0, . . . , N unknowns, together with \delta non-local boundary conditions, we obtained (N + 1)- linear equations. The accuracy and effectiveness of the scheme was tested on some selected problems from the literature. Judging from the table of results and figures, we observed that the approximate solution corresponding to the problem that has exact solution in polynomial form gives a closed form solution while problem with non-polynomial exact solution gives better accuracy compared to the existing results.
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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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    Heat transfer analysis of thermal radiative over a stretching curved surface using molybdenum disulfide and silicon dioxide composite material under the influence of solar radiation
    (2024) Adebowale Martins Obalalu; Adil Darvesh; Lateefat Aselebe; Sulyman Olakunle Salawu; Kazeem Issa
    PurposeThe primary focus of this study is to tackle a critical industry issue concerning energy inefficiency. This is achieved through an investigation into enhancing heat transfer in solar radiation phenomena on a curved surface. The problem formulation of governing equations includes the combined effects of thermal relaxation, Newtonian heating, radiation mechanism, and Darcy-Forchheimer to enhance the uniqueness of the model. This research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilizing the above-mentioned phenomenon with a purpose of advancing thermal technology. A mixture of silicon dioxide (SiO_2)\ and Molybdenum disulfide (MoS_2) is considered for the nanoparticle’s thermal propagation in base solvent propylene glycol. The simulation of the modeled equations is solved using the Shifted Legendre collocation scheme (SLCS). The findings show that, the solar radiation effects boosted the heating performance of the hybrid nanofluid. Furthermore, the heat transmission progress increases against the curvature and thermal relaxation parameter.Design/methodology/approachShifted Legendre collocation scheme (SLCS) is utilized to solve the simulation of the modeled equations.FindingsThe findings show that, the solar radiation effects boosted the heating performance of the hybrid nanofluid. The heat transmission progress increase against the curvature and thermal relaxation parameter.Originality/valueThis research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilizing the above-mentioned phenomenon with a purpose of advancing thermal technology.
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    NUMERICAL SIMULATION OF ENTROPY GENERATION FOR CASSON FLUID FLOW THROUGH PERMEABLE WALLS AND CONVECTIVE HEATING WITH THERMAL RADIATION EFFECT
    (2020) Obalalu Adebowale Martins; Kazeem Issa; Abdulrazaq Abdulraheem; Ajala Olusegun Adebayo; Adeosun Adeshina Taofeeq; Oluwaseyi Aliu; Adebayo Lawal Lanre; Wahaab Adisa Fatai
    In this work, the influence of entropy generation analysis for an electrically conducting Casson fluid flow with convective boundary conditions has been numerically studied. The governing equations are analyzed numerically using weighted residual methods. Subsequently, the residuals were minimized using two different approaches of weighted residual method namely collocation weighted residual method (CWRM) and Galerkin weighted residual method (GWRM) and computed numerically using MATHEMATICAL software. The impacts of governing parameters on Casson flow velocity, temperature profile, local skin friction, and Nusselt number were analysed. The obtained solutions were used to determine the heat transfer irreversibility and bejan number of the model. The results of the computation show that the effect of thermophysical properties such as thermal radiation parameter, suction/injection parameter, magnetic field parameter, radiation parameter, and Eckert number has a significant influence on Skin friction coefficient (Cf) and local Nusselt number (Nu) when compared to the Newtonian fluid. The findings from this study are relevant to advances in viscoelasticity and enhanced oil recovery.
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    Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials
    (Department of Mathematics, Modibbo Adama University, 2024-05) Kazeem Issa; Muritala H. Sulaiman; Esther O. Olabamidele; Ayinde M. Abdullahib
    In this article, the Galerkin-Vieta-Lucas scheme is presented to find an approximate solution to the generalised delay integro-differential equation using the Vieta-Lucas polynomial as an approximation. The Galerkin approach transforms the delay integro-differential equation into a set of n × (n + m) algebraic equations, which, together with the attached conditions, give (n + m) × (n + m) equations. The effectiveness and accuracy of the proposed technique were tested on some existing examples in the literature, and obviously, the results obtained justify the accuracy of the proposed scheme.
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    Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials
    (2020-12-30) Kazeem Issa; Babatunde M. Yisa; Jafar Biazar
    This paper is concerned with numerical approach for solving space fractional diffusion equation using shifted Gegenbauer polynomials, where the fractional derivatives are expressed in Caputo sense. The properties of Gegenbauer polynomials are exploited to reduce space fractional diffusion equation to a system of ordinary differential equations, that are then solved using finite difference method. Some selected numerical simulations of space fractional diffusion equations are presented and the results are compared with the exact solution, also with the results obtained via other methods in the literature. The comparison reveals that the proposed method is reliable, effective and accurate. All the computations were carried out using Matlab package.