Mathematics

Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/100

Mathematics

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Start date: 2024

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Now showing 1 - 10 of 15
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    Numerical Solution for Magnetohydrodynamics Mixed Convection Flow Near a Vertical Porous Plate Under the Influence of Magnetic Effect and Velocity Ratio
    (Maths Model Research Group, FUT, Minna, Nigeria, 2024-02-18) Ibrahim Yusuf; Umaru Mohammed; Khadeejah James Audu
    This paper investigates the effects of thermal radiation on MHD mixed convection flow, heat and mass transfer, Dufour and Soret effects over a porous plate having convective boundary condition under the influence of magnetic field. The governing boundary layer equations are formulated and transformed into nonlinear ordinary differential equations using similarity transformation and numerical solution is obtained by using Runge-Kutta fourth order scheme with shooting technique. The effects of various physical parameters such as velocity ratio parameter, mixed convection parameter, melting parameter, suction parameter, injection parameters, Biot number, magnetic parameter, Schmit and pranditl numbers on velocity and temperature distributions are presented through graphs and discussed.
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    Linear Programming for Profit Maximization of Agricultural Stock
    (Maths Model Research Group, FUT, Minna, Nigeria, 2024-02-18) Jacob Rebeccal; Nyor Ngutor; Khadeejah James Audu
    This paper discusses a few common issues that are specific to agricultural investing, such as the challenge of choosing which stocks to buy in order to maximize returns. The linear programming model was applied to ten (10) agricultural stocks, and the simplex approach was used as the numerical technique to calculate the best possible outcome. The TORA programmer was used to verify the best option, and the findings indicated that not every item should be invested order to maximize profit.
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    Numerical Solutions of Higher Order Differential Equations via New Iterative Method
    (Maths Model Research Group, FUT, Minna, Nigeria, 2024-02-18) Khadeejah James Audu
    Higher order differential equations play a fundamental role in various scientific and engineering disciplines, but their numerical solutions often pose formidable challenges. The New Iterative Method (NIM) has emerged as a promising technique for addressing these challenges. This study is to explore and assess the efficiency and accuracy of New Iterative Method in solving higher-order differential equations. By applying NIM to a range of problems from diverse scientific disciplines, we aim to provide insights into the method's adaptability and its potential to revolutionize numerical analysis. The method is well-suited for numerically integrating both and nonlinear higher-order differential equations. To showcase the efficiency and accuracy of this approach, some numerical tests have been conducted, comparing it to existing methods. The numerical results obtained from these tests strongly suggest that the new iterative scheme outperforms the previously employed method in estimating higher-order problems, thus confirming its convergence.
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    Numerical Assessment of Some Semi-Analytical Techniques for Solving a Fractional-Order Leptospirosis Model.
    (University of Malaysia, 2024-09-30) Khadeejah James Audu; AbdGafar Tunde Tiamiyu; Jeremiah Nsikak Akpabio; Hijaz Ahmad; Majeed Adebayo Olabiyi
    This research aims to apply and compare two semi-analytical techniques, the Variational Iterative Method (VIM) and the New Iterative Method (NIM), for solving a pre-formulated mathematical model of Fractional-order Leptospirosis. Leptospirosis is a significant bacterial infection affecting humans and animals. By implementing the VIM and NIM algorithms, numerical experiments are conducted to solve the leptospirosis model. Comparing the obtained findings demonstrates that VIM and NIM are effective semi-analytical methods for solving systems of fractional differential equations. Notably, our study unveils a crucial dynamic in the disease's spread. The application of VIM and NIM offers a refined depiction of the biological dynamics, highlighting that the susceptible human population gradually decreases, the infectious human population declines, the recovered human population increases, and a significant rise in the infected vector population is observed over time. This nuanced portrayal of the disease's dynamics is crucial for understanding the intricate interplay of Leptospirosis among human and vector populations. The study's outcomes contribute valuable insights into the applicability and performance of the methods in solving the Fractional Leptospirosis model. Results indicate rapid convergence and comparable outcomes for both methods.
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    Stability Analysis of the Disease-Free Equilibrium State of a Mathematical Model of Measles Transmission Dynamics
    (Proceedings of 2nd International Conference on Mathematical Modelling, Optimization and Analysis of Disease Dynamics (ICMMOADD) 2025. Federal University of Technology, Minna, Nigeria, 2025-02-20) Adama, P. W.; Somma, Samuel Abu
    Measles is an acute viral infectious disease caused by the Measles morbillivirus, a member of the paramyxovirus family. The virus is primarily transmitted through direct contact and airborne droplets. In this study, a mathematical model was developed to examine the transmission dynamics of measles and explore effective control measures. The stability of measles-free equilibrium was analyzed, and the results indicate that the equilibrium is locally asymptotically stable when the basic reproduction number R0 is less than or equal to unity. Numerical simulations were conducted to validate the analytical findings, demonstrating that measles can be eradicated if a sufficiently high level of treatment is applied to the infected population.
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    Mathematical analysis of a Chlamydia trachomatis with nonlinear incidence and recovery rates
    (Proceedings of 2nd International Conference on Mathematical Modelling, Optimization and Analysis of Disease Dynamics (ICMMOADD) 2025. Federal University of Technology, Minna, Nigeria, 2025-02-20) Ashezua, T. T.; Abu, E. A.; Somma, Samuel Abu
    Chlamydia, one of the commonest sexually transmitted infections (STIs), remain a public health concern in both underdeveloped and developed countries of the world. Chlamydia has caused worrying public health consequences hence much research work is needed to check the spread of the disease in the population. In this paper, a mathematical model for Chlamydia is developed and analyzed with nonlinear incidence and recovery rates. Qualitative analysis of the model shows that the disease-free equilibrium is locally asymptotically stable using the method of linearization. Further, using the comparison theorem method, the disease-free equilibrium is found to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, mathematical analysis of the reproduction number shows that the intervention levels and the maximum per capita recovery rate due to effective treatment has a significant impact in reducing the burden of Chlamydia in the population. Numerical results show a relationship between the transmission rate, intervention levels, maximum per capita recovery rate and the reproduction number. Sensitivity analysis was conducted on the parameters connected to the reproduction number, Rc and results reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the transmission rate, intervention levels and the maximum per capita recovery rate. These parameters need to be checked by healthcare policy makers if the disease must be controlled in the population.
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    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.
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    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.
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    REFORMULATION OF TWO STEP IMPLICIT LINEAR MULTI-STEP BLOCK HYBRID METHOD INTO RUNGE KUTTA TYPE METHOD FOR THE SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEM (IVP)
    (2025) ALIYU Abubakar; MUHAMMAD Raihanatu; ABDULHAKEEM Yusuf
    Second-order ordinary differential equations (ODEs) is unavoidable in scientific and engineering fields. This research focuses on the reformulation of two-step implicit linear multistep block hybrid method into a seven-stage Runge-Kutta type method for the solution of second-order initial value problems (IVPs). A two-step, four-off-grid-point implicit block hybrid collocation method for first-order initial value problems was derived. Its order and error constants were determined, which shows that the schemes were of order 8, 8, 8, 8, 8 and 9 with respective error constants of , , , , . The derived block method was reformulated into a seven-stage Runge-Kutta type method (RKTM) for the solution of first-order ordinary differential equations; this reformulation was extended to handle the required second-order ordinary differential equations. The second-order Runge- Kutta-type method derived was implemented on numerical experiments. The method was found to be better than existing methods in the literature.
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    METHOD INTO RUNGE KUTTA TYPE METHOD FOR FIRST ORDER INITIAL VALUE PROBLEM (IVP)
    (2025-03) Abubakar Aliyu; Raihanatu Muhammad; Abdulhakeem Yusuf
    Problems arises from science and technology are expressed in differential equations. These differential equation are sometimes in ordinary differential equations. Reliability with high accuracy and stability are necessary for a numerical method for the solution of differential equations. This research paper presents the analysis of a reformulated block hybrid linear multistep method into Runge-Kutta type method (RKTM) for first order initial value problems (IVPs). In view of this, the block hybrid method derived is of uniform order 6 with error constants of , , , and while the Runge-Kutta type method reformulated maintain the order of the derived block hybrid linear multistep method which are of uniform order 6 but with error constants of . Testing for convergence of both the derived block hybrid linear multistep method and the Runge-Kutta type method shows that the two methods are consistent and are also zero stable