Browsing by Author "JIMOH, OMANANYI RAZAQ"

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A Homotopy-Perturbation analysis of the non-linear contaminant transport problem in one dimension with an initial continuous point source.
(NIGERIAN JOURNAL OF TECHNOLOGICAL RESEARCH (NJTR), 2013-02-28) Aiyesimi, Y. M.; JIMOH, OMANANYI RAZAQ
In this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized 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 by homotopy-perturbation method. Graphs are plotted using the solution obtained from the method and the results are presented, discussed and interpreted. The research findings show that the concentration increases with time and decreases as distance increases.
A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer
(Universal Journal of Applied Mathematics, 2013-12-10) Rasaq O. Olayiwola; JIMOH, OMANANYI RAZAQ; Abdulhakeem Yusuf; Samuel Abubakar
A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.
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.
Agreement between the Homotopy Perturbation Method and Variation Iterational Method on the Analysis of One-Dimensional Flow Incorporating First Order Decay
(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2019-06-28) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.
In this paper, a comparative study of reactive contaminant flow for constant initial concentration in one dimension is presented. The adsorption term is modeled by Freudlich Isotherm. An approximation of the one-dimensional contaminant flow model was obtained using homotopy-perturbation transformation and the resulting linear equations were solved semi-analytically by homotopyperturbation method (HPM) and Variational Iteration Method (VIM). Graphs were plotted using the solution obtained from the methods and the results presented and discussed. The analysis of the results obtained show that the concentration of the contaminant decreases with time and distance as it moves away from the origin.
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.
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.
Approximate Solution of SIR Infectious Disease Model Using Homotopy Perturbation Method (HPM).
(The Pacific Journal of Science and Technology, 2013-11-13) S. Abubakar; N.I. Akinwande; JIMOH, OMANANYI RAZAQ; F.A. Oguntolu; O.D. Ogwumu
In this paper we proposed a SIR model for general infectious disease dynamics. The analytical solution is obtained using the Homotopy Perturbation Method (HPM). We used the MATLAB computer software package to obtain the graphical profiles of the three compartments while varying some salient parameters. The analysis revealed that the efforts at eradication or reduction of disease prevalence must always match or even supersede the infection rate.
APPROXIMATE SOLUTIONS FOR MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE CLASS
(Transactions of the Nigerian Association of Mathematical Physics, 2021-03-14) Somma S. A.; Akinwande N. I.; Ashezua T. T.; Nyor N.; JIMOH, OMANANYI RAZAQ; Zhiri A. B.
In this paper we used Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM and (ADM) obtained were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. The solutions were also presented graphically to give more insight into the dynamics of the monkeypox virus. It was observed that the two solutions were in agreement with each other and also with Runge-Kutta.
Behaviour of Contaminant in a Flow due to Variations in the Cross-Flow dispersion under a Dirichlet Boundary Conditions.
(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2024-04-18) JIMOH, OMANANYI RAZAQ; Adebayo A.; Salihu, N. O.; Bako, D.
The advection-dispersion equation (ADE) is mostly adopted in evaluating solute migration in a flow. This study presents the behavior of contaminant in a flow due to variations in the cross-flow dispersion under a Dirichlet boundary conditions. The 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 was obtained. In deriving the model equation, it was assumed that there was a constant point-source concentration at the origin and a Dirichlet type boundary condition at the exit boundary. The cross-flow dispersion coefficients, velocities and decay terms are time-dependent. The modeled equation was transformed using some space and time variables 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 cross-flow coefficient decline the concentration of the contaminant with respect to increase in time, vertical distance and horizontal distance in different patterns.
CHEBYSHEV COLLOCATION APPROACH FOR CONTINUOUS FOUR-STEP HYBRID BACKWARD DIFFERENCE FORMULA FOR STIFF SYSTEM
(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2019-09-15) MOHAMMED, U.; AJINUHI, J. O.; JIMOH, OMANANYI RAZAQ; DAUDA, A. A.; AKINTUBUBO, B. G.
In this paper, we developed an implicit continuous four-step hybrid backward difference formulae for the direct solution of stiff system. For this purpose, the Chebyshev polynomial was employed as the basis function for the development of schemes in a collocation and interpolation techniques. The schemes were analysed using appropriate existing theorem to investigate their stability, consistency, convergence and the investigation shows that the developed schemes are consistent, zero-stable and hence convergent. The methods were implemented on test problem from the literatures to show the accuracy and effectiveness of the scheme.
Comparative Analysis of a Non-Reactive Contaminant Flow Problem for Constant Initial Concentration in Two Dimensions by Homotopy-Perturbation and Variational Iteration Methods.
(Pacific Journal of Science and Technology, 2013-05-10) JIMOH, OMANANYI RAZAQ
In this paper, we present a comparative analysis of non-reactive contaminant flow problem for constant initial concentration in two dimensions by homotopy-perturbation and Variational Iteration method. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically by homotopy-perturbation method (HPM) and Variational Iteration Method (VIM). Graphs are plotted using the solution obtained from the method and the results are presented and discussed.
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.
EFFECT OF HEAT AND MASS TRANSFER ON MAGNETO-HYDRODYNAMIC FLOW WITH CHEMICAL REACTION AND VISCOUS ENERGY DISSIPATION PAST AN INCLINED POROUS PLATE
(Scientia Africana, 2023-08-22) JIMOH, OMANANYI RAZAQ; Abdullahi, D.
In this paper, a mathematical model describing heat and mass transfer of magneto-hydrodynamic flow with chemical reaction and viscous energy dissipation past an inclined porous plate is presented. The governing partial differential equations which describe the phenomenon were nondimensionalized with the aid of some dimensionless quantities. The dimensionless coupled non-linear partial differential equations were solved using the harmonic solution technique. The results obtained were discussed graphically. Findings from the results obtained reveal that increase in Peclet number; Heat source parameter and Grashof number enhance the velocity profiles. Similarly, an increase in the Peclet energy number, Eckert number, Heat source parameter, angle of inclination, permeability parameter and Stuart number leads to an increase in the temperature profile.
Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium
(Journal of Applied Sciences and Environmental Management (JASEM), 2023-08-23) JIMOH, OMANANYI RAZAQ; IBRAHIM, I
A study on transient free convection flow of a dusty viscous fluid through a porous medium is important for improving the existing industrial processes and for developing new chemical and geothermal systems. This paper presents a mathematical model for transient laminar free convective flow of a dusty viscous fluid through a porous medium in the presence of viscous energy dissipation. The partial differential equations governing the phenomenon were non-dimensionalized using some dimensionless quantities. The dimensionless coupled non-linear partial differential equations were solved using harmonic solution technique. The result obtained were presented graphically and discussed. These results revealed that increase in Peclet number, Eckert number and Grashof number leads to increase in the velocity profile. Increase in the mass concentration of the dust particles, concentration resistance ratio, Eckert number and Peclet number leads to increase in the velocity profile of the dust particles. Increase in the Reynold number leads to a reduction in the velocity profile. Increase in Peclet number, Eckert number and Grashof number leads to increase in temperature profile. Similarly, increase in heat source parameter, coefficient of Grashof number and Reynold number lead to reduction in the temperature profile.
INFLUENCE OF OFF-DIAGONAL DISPERSION ON THE CONCENTRATION OF CONTAMINANT IN A TWO-DIMENSIONAL CONTAMINANT FLOW: A SEMI-ANALYTICAL APPROACH
(Journal of the Nigerian Association of Mathematical Physics, 2018-03-20) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; JIYA, M.; Bolarin G. A.
The equation which describes the two-dimensional contaminant flow model is a partial differential equation characterized by advection, dispersion, adsorption, first order decay and zero-order source. In this paper, the off-diagonal dispersion parameter is introduced into the two dimensional contaminant flow model in order to study its effect on the concentration of the contaminant. It is assumed that the adsorption term is modeled by Freudlich isotherm. The parameter expanding method is applied on the equation to obtain a set of differential equations which are then solved successively using the Eigen functions expansion technique to obtain the analytical solution. The results obtained are plotted into graphs to show the effect of change in the parameters on the concentration of the contaminants. Findings from this research show that the contaminant concentration decreases with increase in distance as the off-diagonal dispersion coefficient, zero-order source coefficient and vertical dispersion coefficient increases.
INFLUENCE OF ZERO-ORDER SOURCE AND DECAY COEFFICIENTS ON THE CONCENTRATION OF CONTAMINANTS IN TWO-DIMENSIONAL CONTAMINANT FLOW
(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2017-04-23) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.; Bolarin, G. A.
In this article, an eigenfunctions expansion method is used in studying the behavior of two-dimensional contaminant flow problem with non-zero initial concentration. The mathematical model describing the contaminant flow 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. Before the application of the eigenfunctions method, the parameter expanding method is applied on the model and the boundary conditions are transformed to the homogeneous type. Thereafter, the approximate solution of the resulting initial value problem was obtained successively. The results obtained are expressed graphically to show the effect of change in the zero-order source and decay coefficients 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 as the zero-order source and decay coefficient increases.
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.
Modelling Thermal Radiation Effects on Temperature and Concentration on Magnetohydrodynamic Flow in the Presence of Chemical Reaction in a Porous Medium
(MATH MODEL RESEARCH GROUP, 2025-02-18) Lawal A. O.; JIMOH, OMANANYI RAZAQ; Yusuf S. I.
This study presents a mathematical model that explores the impact of thermal radiation effects on temperature and concentration on magnetohydrodynamic (MHD) flow in the presence of chemical reaction in a porous medium. The governing partial differential equations were nondimensionalized, transformed to ordinary differential equations using harmonic solution technique and solved using perturbation method. The results which were presented graphically, highlight several key observations. Specifically, an increase in Grashof number, Dufour number, and porosity parameter leads to higher velocity profiles. Furthermore, Radiative parameters are found to reduce the fluid temperature. The findings of this work will be crucial in optimizing processes in areas like combustion, cooling systems and environmental control technology where such complex interactions are prevalent.
Semi-analytical Study of a One-dimensional Contaminant Flow in a Finite Medium
(Journal of Applied Science Environmental Management (JASEM), 2017-05-21) JIMOH, OMANANYI RAZAQ; AIYESIMI, YM; JIYA, M.; BOLARIN, GA
The Bubnov-Galerkin weighted residual method was used to solve a onedimensional contaminant flow problem in this paper. The governing equation of the contaminant flow, which is characterized by advection, dispersion and adsorption was discretized and solved to obtain the semi-analytical solution. The adsorption isotherm was assumed to be of Freudlich type. The results obtained were 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 as the dispersion and velocity coefficient decrease.
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.