Mathematics

Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/200

Mathematics

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Start date: 2020

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Now showing 1 - 10 of 25
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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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    Stability Analysis of the Mathematical Modelling of Transmission and Control of Rabies Incorporating Vaccination Class
    (Dutse Journal of Pure and Applied Sciences (DUJOPAS),, 2022-03-12) Abdurrahman, Nurat Olamide; Somma, S. A.; Balogun R. T.; Eguda F. Y.; Adama, P. W.; Yisa E. M.
    Rabies is a viral disease of the nervous system that is often transmitted to human beings through the bite or scratch of rabid animals. The uprising of insecurity globally has forced several people to get dogs into their homes. This paper formulated the mathematical model of rabies transmission and control by incorporating vaccination class. The model's Disease Free Equilibrium (DFE) state was obtained and used to compute the basic reproduction number R0. Local stability analysis of the DFE was carried out using Jacobian Matrix techniques. The DFE is locally asymptotically stable if R0 < 1.
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    Mathematical Modeling of the Spread of False Information within Social Media
    (Ilorin Journal of Science, 2024-10-15) Abdurrahman, Nurat Olamide; Ibrahim, M. O.; Ibrahim, J. O.
    One of the societal pollutions in our environment that requires overhauling intervention is the spread of false information. In this paper, we modelled the spread of rumor in a continuous and dynamic population of five compartments. We considered an incubation period which allows rumormongers to verify the authenticity of information received before spreading. Stability analysis of the rumor-free equilibrium (RFE) and the rumor-present equilibrium (RPE) was carried out. The RPE is a function of the reproduction number R0. In order to annihilate the rumor, the results suggest that we should reduce R0 continuously below 1. The results are numerically validated and discussed.
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    Homotopy Perturbation Method (HPM) for Solving Mathematical Modelling of Monkey Pox virus
    (National Mathematical Center, 2021-03-22) Abdurrahman, Nurat Olamide; Somma S. A.; Ayegbusi F. D.; Adama P. W.; Gana P.; Eguda F. Y.
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    Direct Solution of 𝒚′′(𝒙) = 𝒇(𝒙, 𝒚, 𝒚′) Using Four Points Block-Hybrid Linear Multistep Method of Order Seven with Applications
    (WORLD SCIENTIFIC NEWS, 2022-11) A. A. Oyedeji; R. Muhammad
    The study aims to construct an implicit block hybrid method with four points to tackle general second order initial value problems of ordinary differential equations (ODEs) directly. Power series is used as the basis function to obtain the proposed method which involved the first and second derivatives of 𝑓(𝑥, 𝑦, 𝑦′). From the investigation done, it was found that the proposed method is consistent and zerostable, hence it is convergent. The proposed method’s efficiency was obtained and a comparison was made in terms of accuracy to some existing methods with similar order and the ones higher than it. The new proposed method is able to solve linear, nonlinear and systems of equations of general second order Initial Value Problems and outperformed existing methods with impressive results. Applications of the proposed method to a real-life problem is discussed.
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    AN ANALYSIS OF ALGEBRAIC PATTERN OF A FIRST ORDER AND AN EXTENDED SECOND ORDER RUNGE-KUTTA TYPE METHOD
    (Faculty of Science, Kaduna State University, 2020) R. Muhammad,; Y. A. Yahaya; A.S. Abdulkareem
    The algebraic pattern of a 6-Stage Block Hybrid Runge –Kutta Type Methods (BHRKTM) for the solution of Ordinary Differential Equations (ODEs) is carefully analyzed. The analysis of the methods expressed in the Butcher Tableau led to the evolvement of two equations that satisfy the Runge – Kutta consistency conditions. The reason behind the uniform order and error constant for the developed first order and extended second order methods is explained using the theory of linear transformation and monomorphism. The pattern was retained during the transformation.
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    Mathematical modelling of solid waste management
    (International Journal of Mathematical Analysis and Modelling, 2023-07-21) Abdurrahman, Nurat Olamide; Ibrahim, Mohammed Olanrewaju
    Solid waste is anything that comes from domestic, commercial, or industrial sources that is no longer needed. It is deposited as undesired. Waste disposal did not become an issue when there were few habitations and a lot of open space. Waste disposal becomes a real concern in towns and cities when more individuals move there in pursuit of employment [6,12]. Using a set of ordinary differential equations, a mathematical model for managing solid waste is put forth in this study. The solution’s existence and uniqueness are proven. In order to simulate the sensitive parameter for solid waste management, the next-generation matrix is used to identify the basic reproduction number R0. It has been found that when waste production increases, so does the rate at which energy is produced from waste.