Mathematics
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Mathematics
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Item Comparison of Refinement Accelerated Relaxation Iterative Techniques and Conjugate Gradient Technique for Linear Systems.(Mathematical Association of Nigeria (MAN), 2023-08-20) Khaddejah James AuduIterative methods use consecutive approximations to get more accurate results. A comparison of three iterative approaches to solving linear systems of this type 𝑀𝑦=𝐵 is provided in this paper. We surveyed the Refinement Accelerated Relaxation technique, Refinement Extended Accelerated Relaxation technique, and Conjugate Gradient technique, and demonstrated algorithms for each of these approaches in order to get to the solutions more quickly. The algorithms are then transformed into the Python language and used as iterative methods to solve these linear systems. Some numerical investigations were carried out to examine and compare their convergence speeds. Based on performance metrics such as convergence time, number of iterations required to converge, storage, and accuracy, the research demonstrates that the conjugate gradient method is superior to other approaches, and it is important to highlight that the conjugate gradient technique is not stationary. These methods can help in situations that are similar to finite differences, finite element methods for solving partial differential equations, circuit and structural analysis. Based on the results of this study, iteration techniques will be used to help analysts understand systems of linear algebraic equationsItem A groundwater-based irrigation modeling system that optimizing water use efficiency and ensuring long-term sustainability of groundwater resources.(Maths Model Research Group, FUT, Minna, Nigeria, 2025-03-20) Y. Y. Alheri; N. Nyor; Khadeejah James AuduItem Numerical Assessment of Some Almost Runge-Kutta and Runge-Kutta Methods for First- Order Differential Equation(Maths Model Research Group. FUT, Minna, Nigeria, 2025-02-20) Khadeejah James Audu; Muideen Taiwo Kharashi; Yusuph Amuda Yahaya; James Nkereuwem Essien; Abraham Ajeolu OluwasegunNumerical methods play a critical role in solving first-order Ordinary Differential Equations (ODEs), with their efficiency and accuracy being key considerations. This study conducts a detailed comparative analysis of four numerical schemes: the Almost Runge-Kutta fourth-order scheme (ARK4), the Almost Runge-Kutta third-order fourth-stage scheme (ARK34), the classical Runge- Kutta fourth-order scheme (RK4), and the Runge-Kutta fourth-order fifth-stage scheme (RK45). The methods are evaluated based on their computational accuracy, error behavior, and efficiency. Numerical experiments reveal that all methods deliver highly accurate solutions, with ARK4 emerging as the most effective due to its lower computational complexity. ARK4 demonstrates superior performance in achieving minimal absolute error with reduced computational effort, making it a suitable choice for solving first-order ODEs. This study highlights ARK4 as a viable alternative to conventional Runge-Kutta methods for practical applications.Item Stability and Bifurcation Analysis of a Mathematical Modeling of Measles Incorporating Vitamin a Supplement(Sule Lamido University Journal of Science and Technology (SLUJST), 2021-01-20) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.; Ogwumu, O. D.; Ashezua, T. T.; Eguda, F. YMeasles is transmissible disease that is common among children. The death caused by measles among children of five years and below is alarming in spite of the safe and effective vaccine. It has been discovered that Vitamin A Deficiency (VAD) in children increases their chances of measles infection. In this paper, the mathematical model of measles incorporating Vitamin A supplement as treatment was formulated and analyzed. The equilibrium points are obtained and analyzed for stability. Bifurcation and sensitivity analyses were carried out to gain further insight into the spread and control of measles. The stability analysis revealed that Disease Free Equilibrium (DFE) is stable if R0 1. The bifurcation analysis revealed forward bifurcation while the sensitivity analysis shows the most sensitive parameters of the model that are responsible for the spread and control of the diseases. The effect of sensitive parameters on Basic Reproduction Number, 0 R were presented graphically. Vaccination, recovery and Vitamin A supplement rates have been shown from the graphical presentation as the important parameter that will eradicate the measles from the population while contact and loss of immunity rates have shown that measles will persist in the population. People should be sensitized on the danger of living with infected persons. Government should do more in routine immunization and administration of Vitamin A Supplement.Item Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM)(Pacific Journal of Science and Technology (PJST), 2013-12-25) Abubakar, Samuel; Akinwande, N. I.; Jimoh, O. R.; Oguntolu, F. A.; Ogwumu, O. D.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.Item Stability Analysis of Disease Free Equilibrium (DFE) State of a Mathematical Model of Yellow Fever Incorporating Secondary Host(Pacific Journal of Science and Technology, 2017-12-28) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahaman, S.In this paper we formulate a mathematical model of yellow fever incorporating secondary host. We obtained the Disease Free Equilibrium (DFE) Points and compute the basic reproduction number. The local and global stability of the DFE was analyzed using Jacobian Matrix stability techniques and Lyapunov function respectively. The local and global stability was asymptotically stable if 1 0 R and 1 0 R , respectively. The basic reproduction number and control parameters of the model were presented graphically.Item Mathematical Modeling of Algae Population Dynamics on the Surface of Water(Pacific Journal of Science and Technology, 2019-12-30) Abdurrahman, N. O.; Akinwande, N .I.; Somma, Samuel AbuThe paper presented an analytical solution of the exponential growth model of algae population dynamics on the water surface. The Computer Symbolic Algebraic Package, MAPLE is used to simulate the graphical profiles of the population with time while varying the parameters, such as diffusion and rate of change of algae density, governing the subsistence or extinction of the water organisms.Item Semi-Analytical Solution for the Mathematical Modeling of Yellow Fever Dynamics Incorporating Secondary Host(Communication in Mathematical Modeling and Applications, 2019-02-20) Somma, Samuel Abu; Akinwande, N. I.,; Abah, R. T.; Oguntolu, F. A.; Ayegbusi, F. D.In this paper we use Differential Transformation Method (DTM) to solve the mathematical modeling of yellow fever dynamics incorporating secondary host. The DTM numerical solution was compared with the MAPLE RungeKutta 4-th order. The variable and parameter values used for analytical solution were estimated from the data obtained from World Health Organization (WHO) and UNICEF. The results obtained are in good agreement with Runge-Kutta. The solution was also presented graphically and gives better understanding of the model. The graphical solution showed that vaccination rate and recovery rate play a vital role in eradicating the yellow fever in a community.Item A 3-Person Non-Zero-Sum Game for Sachet Water Companies(Asian Research Journal of Mathematics, 2022-08-12) Nyor, N.; Muazu, M. I.; Somma, Samuel AbuThe business of Sachet water (popularly called pure water) in Nigeria is often competitive due to the high demand for Sachet water by the populace. This is so because sachet water is the most affordable form of pure drinking water in Nigeria. As such, Sachet Water Firms that want to succeed in an ever increasing competitive market need to have the knowledge of Game Theory to identify which strategy will yield better profit independent of the strategy adopted by other competitors. This paper is aimed to investigate and determine the equilibrium point for three Sachet Water Firms using the Nash Equilibrium Method as it provides a systematic approach for deciding the best strategy in competitive situation. The result showed two Nash Equilibriums (promo, promo) and (stay-put, stay-put) with their respective payoffs of (82; 82; 82) and (147; 147; 147).Item Modelling the Impacts of Media Campaign and Double Dose Vaccination in Controlling COVID-19 in Nigeria(Alexandria Engineering Journal, 2023-01-15) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and noncompliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (𝑅𝑚𝑣). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever 𝑅𝑚𝑣 ≤ 1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((𝑅0 ≥ 7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at 𝑅0 = 4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin’s maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a firstdose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.