School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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Author: search.filters.author.JIMOH, OMANANYI RAZAQHas files: Yes

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    Mathematical Analysis of a Contaminant Flow in a Finite Medium using the Weighted Residual Method
    (Ilorin Journal of Science, 2015-02-01) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.; Bolarin, G. A.
    In this paper, a Galerkin weighted Residual method is used in providing an analytical solution of two-dimensional contaminant flow problem with non-zero initial concentration. The equation is described by advection, dispersion, adsorption, first order decay and zero-order source. It is assumed that the adsorption term is modeled by Freudlich isotherm. Using Bubnov-Galerkin method, the governing equation was converted to a discrete problem. Thereafter, the approximate solution of the resulting system of initial value problem was obtained. The results obtained are expressed in graphical form to show the effect of change in the parameters on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin while it increases with increase in the zero-order source coefficient.
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    Solution of One-Dimensional Contaminant Flow Problem Incorporating the Zero Order Source Parameter by Method of Eigen-Functions Expansion
    (JOURNAL OF APPLIED SCIENCES AND ENVIROMENTAL MANAGEMENT (JASEM), 2021-10-25) JIMOH, OMANANYI RAZAQ; SHUAIBU, BN
    A semi – analytical study of a time dependent one – dimensional advection – dispersion equation (ADE) with Neumann homogenous boundary conditions for studying contaminants flow in a homogenous porous media is presented. The governing equation which is a partial differential equation incorporates the advection, hydrodynamic dispersion, first order decay and a zero order source effects in the model formulation. The velocity of the flow was considered exponential in nature. The solution was obtained using Eigen function expansion technique after a suitable transformation. The results which investigate the effect change in the parameters on the concentration were discussed and represented graphically. The study revealed that as the zero order source coefficient increases, the contaminant concentration decreases with time.
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    ANALYTICAL STUDY OF THE EFFECT OF CHANGE IN DECAY PARAMETER ON THE CONTAMINANT FLOW UNDER THE NEUMANN BOUNDARY CONDITIONS
    (Transactions of the Nigerian Association of Mathematical Physics, 2021-04-15) JIMOH, OMANANYI RAZAQ; Adebayo A.
    The advection-dispersion equation is commonly employed in studying solute migration in a flow. This study presents an analytical solution of a two-dimensional advection-dispersion equation for evaluating groundwater contamination in a homogeneous finite medium which is initially assumed not contaminant free. In deriving the model equation, it was assumed that there was a constant point-source concentration at the origin and a flux type boundary condition at the exit boundary. The cross-flow dispersion coefficients, velocities and decay terms are time-dependent. The modeled equation was transformed and solved by parameter expanding and Eigen-functions expansion method. Graphs were plotted to study the behavior of the contaminant in the flow. The results showed that increase in the decay coefficient declines the concentration of the contaminant in the flow.
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    AN OPTIMIZED SINGLE-STEP BLOCK HYBRID NYSTRÖM-TYPE METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS OF BRATU-TYPE
    (African Journal of Mathematics and Statistics Studies, 2023-10-12) Ajinuhi J.O.; Mohammed U.; Enagi A.I.; JIMOH, OMANANYI RAZAQ
    In this paper, a global single-step implicit block hybrid Nyström-type method (BHNTM) for solving nonlinear second-order initial-boundary value problems of Bratu-type is developed. The mathematical derivation of the proposed BHNTM is based on the interpolation and multistep collocation techniques with power series polynomials as the trial function. Unlike previous approaches, BHNTM is applied without linearization or restrictive assumptions. The basic properties of the proposed method, such as zero stability, consistency and convergence are analysed. The numerical results from three test problems demonstrate its superiority over existing methods which emphasize the effectiveness and reliability in numerical simulations. Furthermore, as the step size decreases as seen in the test problems, the error drastically reduces, indicating BHNTM's precision. These findings underscore BHNTM's significance in numerical methods for solving differential equations, offering a more precise and dependable approach for addressing complex problems.
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    A Novel Seventh-Order Implicit Block Hybrid Nyström-Type Method for Second- Order Boundary Value Problems
    (INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI), 2023-11-05) Joel Olusegun Ajinuhi; Umaru Mohammed; Abdullah Idris Enagi; JIMOH, OMANANYI RAZAQ
    This paper introduces a novel approach for solving second-order nonlinear differential equations, with a primary focus on the Bratu problem, which holds significant importance in diverse scientific areas. Existing methods for solving this problem have limitations, prompting the development of the Block Hybrid Nystrom-Type Method (BHNTM). BHNTM utilizes the Bhaskara points derived, using the Bhaskara cosine approximation formula. The method seeks a numerical solution in the form of a power series polynomial, efficiently determining coefficients. The paper discusses BHNTM's convergence, zero stability, and consistency properties, substantiated through numerical experiments, highlighting its accuracy as a solver for Bratu-type equations. This research contributes to the field of numerical analysis by offering an alternative, effective approach to tackle complex second-order nonlinear differential equations, addressing critical challenges in various scientific domains.
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    Computational Analysis of a one-dimensional nonlinear reactive contaminant flow with an initial continuous point source by homotopy-perturbation method.
    (Journal of the Nigerian Association of Mathematical Physics, 2012-11-05) Aiyesimi, Y. M.; JIMOH, OMANANYI RAZAQ
    In this paper, a Homotopy-perturbation analysis of a non–linear reactive contaminant flow equation with initial continuous point source is provided. The equation is described by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically. The graphs of the concentration against the distance, reaction parameter and time are presented and analyzed to determine the effects of increase in the reaction coefficient, time and distance on the concentration. Findings from this research show that the concentration of the contaminant decreases with time and decreases faster when the value of the reaction parameter α is high.