School of Physical Sciences (SPS)
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Item A 3-Person Non-Zero-Sum Game for Sachet Water Companies(Asian Research Journal of Mathematics, 2022-06-24) 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 A 3-step block hybrid backward differentiation formulae (bhbdf) for the solution of general second order ordinary differential equation(New Trends in Mathematical Sciences, 2021-07-12) Hussaini Alhassan; Muhammad RaihanatuIn this paper, the block hybrid Backward Differentiation formulae (BHBDF) for the step number k=3 is developed using power series as basis function for the solution of general second order ordinary differential equation. The idea of interpolation and collocation of the power series at some selected grid and off- grid points gave rise to continuous schemes which were further evaluated at those points to produce discrete schemes combined together to form block methods. Numerical problems were solved with the proposed methods and were found to perform effectively.Item A 4-STAGE RUNGE-KUTTA TYPE METHOD FOR SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS(Pan-American Journal of Mathematics, 2024) RAIHANATU MUHAMMAD; ABDULMALIK OYEDEJIIn this paper, a 2 step implicit block hybrid linear multistep method was reformulated into a 4-stage block hybrid Runge-Kutta Type Method via the butcher analysis. The method can be used to solve first order stiff ordinary differential equations. A numerical example solved with the proposed method showed a better result in comparison with an existing methodItem A Backward Diffrention Formula For Third-Order Inttial or Boundary Values Problems Using Collocation Method(Islamic Azad University,Rasht ', Iran, 2021-09-19) AbdGafar Tunde Tiamiyu; Abosede Temilade Cole; Khadeejah James AuduWe propose a new self-starting sixth-order hybrid block linear multistep method using backward differentiation formula for direct solution of third-order differential equations with either initial conditions or boundary conditions. The method used collocation and interpolation techniques with three off-step points and five-step points, choosing power series as the basis function. The convergence of the method is established, and three numerical experiments of initial and boundary value problems are used to demonstrate the efficiency of the proposed method. The numerical results in Tables and Figures show the efficiency of the method. Furthermore, the numerical method outperformed the results from existing literature in terms of accuracy as evident in the results of absolute errors producedItem A Mathematical Model of a Yellow Fever Dynamics with Vaccination(Journal of the Nigerian Association of Mathematical Physics, 2015-11) F. A. Oguntolu; N. I. Akinwande; S. A. Somma; F. Y. Eguda; T. T. AshezuaIn this paper, a mathematical model describing the dynamics of yellow fever epidemics, which involves the interactions of two principal communities of Hosts (Humans) and vectors (mosquitoes) is considered. The existence and uniqueness of solutions of the model were examined by actual solution. We conduct local stability analysis for the model. The results show that it is stable under certain conditions. The system of equations describing the phenomenon was solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It is discovered that improvement in Vaccination strategies will eradicate the epidemics.Item A protocol for setting dose reference level for medical radiography in Nigeria: A Review(BAYERO UNIVERSITY, KANO, NIGERIA, 2010-02-10) OLARINOYE, OYELEKE; SHARIFAT IPatients’ dose audit reports in some Nigerian hospitals had shown large inter- and intra-hospital variations for the same radiological examinations. They have thus presented the need, to have a national standard for radiological diagnostic procedures and set dose limits for individual x-ray examination centers in Nigeria. These will go a long way in reducing inter- and intra-hospital dose range factors, thus reducing doses to as low as reasonably achievable and consistent with clinical objectives of the examinations. In establishing a national dose limit for medical radiological examinations, there is a need to have a national dose survey. This paper suggests a Reasonable and easy procedure for achieving a national radiological dose survey. Due to its simplicity of measurement, the use of entrance surface dose as the dose parameter to be used for setting the dose limit as recommended by the European Union and the International Atomic Energy Agency (IAEA) is also suggested. ESD can be measured directly through the use of solid state detectors, or indirectly by measuring free air exposure which can later be converted to ESD using standard formula. The methods of measuring the entrance surface dose and how to derive the dose limit from them are also highlighted.Item A review of coating tin oxide electron transport layer for optimizing the performance of perovskite solar cells(Chemistry of Inorganic Materials Volume 6, August 2025, 100100, 2025-04-10) YUSUF Abubakar Sadiq; Ahmad Alhaji Abubakar; Isah Kimpa Mohammed; Umaru Ahmadu; Kasim Uthman IsahPerovskite solar cells (PSCs) have recently emerged as a transformative technology in the photovoltaic sector, drawing considerable attention due to their rapid advancements in power conversion efficiency (PCE), which now exceeds 26.7 %. This efficiency level places them in direct competition with conventional silicon-based solar cells. A key element in ensuring the high performance of PSCs is the charge transport layer (CTL), particularly the electron transport layer (ETL). The ETL plays a crucial role by efficiently collecting photo-generated electrons from the perovskite layer and transferring them to the transparent conductive oxide electrode. Among the ma- terials used for ETLs, tin oxide (SnO 2) stands out for its wide band gap, excellent optical transparency, superior carrier mobility, and remarkable chemical stability. Additionally, SnO2 can be deposited at low temperatures, making it ideal for mass production and adaptable for applications such as flexible devices. Despite its inherent advantages, the overall performance and quality of the ETL, and thus the device itself, are heavily influenced by the fabrication process. This study reviews recent approaches to fabricating SnO 2 ETLs in PSCs, with a focus on optimizing efficiency and long-term stabilityItem A Sixth Order Implicit Hybrid Backward Differentiation Formulae (HBDF) for Block Solution of Ordinary Differential Equations(American Journal of Mathematics and Statistics, 2012) Muhammad R; Yahaya.Y.AThe Hybrid Backward Differentiation Formula (HBDF) for case K=5 was reformulated into continuous form using the idea of multistep collocation. Multistep Collocation is a continuous finite difference (CFD) approximation method by the idea of interpolation and collocation. The hybrid 5-step Backward Differentiation Formula (BDF) and additional methods of order (6,6,6,6,6,)𝑇𝑇 were obtained from the same continuous scheme and assembled into a block matrix equation which was applied to provide the solutions of IVPs over non-overlapping intervals.The continous form was im-mediately employed as block methods for direct solution of Ordinary Differential Equation (𝑦𝑦′=𝑓𝑓(𝑥𝑥,𝑦𝑦)). Some benefits of this study are, the proposed block methods will be self starting and does not call for special predictor to estimate 𝑦𝑦’ in the integrators and all the discrete methods obtained will be evaluated from a single continuous formula and its derivatives at various grids and off grid points. These study results help to speed up computation, also the requirement of a starting value and the overlap of solution model which are normally associated with conventional Linear Multistep Methods were elimi-nated by this approach. In conclusion, a convergence analysis of the derived hybrid schemes to establish their effectiveness and reliability was presented. Numerical example carried out on stiff problem further substantiates their performance.Item A THIRD REFINEMENT OF JACOBI METHOD FOR SOLUTIONS TO SYSTEM OF LINEAR EQUATIONS(Federal University, Dutsin Ma, Nigeria, 2023-10-15) Khadeejah James Audu; James Nkereuwem Essien; Abraham Baba Zhiri; Aliyu Rasheed TaiwoSolving linear systems of equations stands as one of the fundamental challenges in linear algebra, given their prevalence across various fields. The demand for an efficient and rapid method capable of addressing diverse linear systems remains evident. In scenarios involving large and sparse systems, iterative techniques come into play to deliver solutions. This research paper contributes by introducing a refinement to the existing Jacobi method, referred to as the "Third Refinement of Jacobi Method." This novel iterative approach exhibits its validity when applied to coefficient matrices exhibiting characteristics such as symmetry, positive definiteness, strict diagonal dominance, and 𝑀 -matrix properties. Importantly, the proposed method significantly reduces the spectral radius, thereby curtailing the number of iterations and substantially enhancing the rate of convergence. Numerical experiments were conducted to assess its performance against the original Jacobi method, the second refinement of Jacobi, and the Gauss-Seidel method. The outcomes underscore the "Third Refinement of Jacobi" method's potential to enhance the efficiency of linear system solving, thereby making it a valuable addition to the toolkit of numerical methodologies in scientific and engineering domains.Item Advancements in Solving Higher-Order Ordinary Differential Equations via the Variational Iterative Method.(Akdeniz University, Turkey, 2025-12-30) Khadeejah James Audu; Michael Ogbole Ogwuche; Sıkırulaı Abolaji Akande; Yahaya Yusuph AmudaThis study presents advancements in solving higher-order ordinary differential equations (ODEs) using the Variational Iterative Method (VIM) and compares its performance with the New Iteration Method (NIM) and Adomian Decomposition Method (ADM). ODEs are critical in modeling the rate of change in various systems over time, and many do not have exact solutions, necessitating the use of numerical methods to obtain approximate results. While several iterative methods exist, a detailed comparison of VIM with other techniques, particularly for higher-order ODEs, is still lacking. This research focuses on understanding the principles and methodology of VIM and applying it to solve higher-order linear and nonlinear ODEs. The study evaluates the accuracy, convergence rate, and computational efficiency of VIM compared to NIM and ADM through the solution of third, fourth, and fifth-order differential problems. The results show that VIM outperforms NIM and ADM, with faster convergence and higher efficiency. Error analysis in Figures 1, 2, and 3 highlights the strengths and limitations of each method, providing valuable insights for researchers and practitioners in selecting the most appropriate technique for solving higher-order ODEs. These findings advance the development of iterative methods in numerical analysis and contribute to progress in the field of differential equations.Item An Accelerated Iterative Technique: Third Refinement of Gauss–Seidel Algorithm for Linear Systems(Multidisciplinary Digital Publishing Institute, Switszerland, 2023-04-28) Khaddejah James Audu; James Nkereuwem EssienObtaining an approximation for the majority of sparse linear systems found in engineering and applied sciences requires efficient iteration approaches. Solving such linear systems using iterative techniques is possible, but the number of iterations is high. To acquire approximate solutions with rapid convergence, the need arises to redesign or make changes to the current approaches. In this study, a modified approach, termed the “third refinement” of the Gauss-Seidel algorithm, for solving linear systems is proposed. The primary objective of this research is to optimize for convergence speed by reducing the number of iterations and the spectral radius. Decomposing the coefficient matrix using a standard splitting strategy and performing an interpolation operation on the resulting simpler matrices led to the development of the proposed method. We investigated and established the convergence of the proposed accelerated technique for some classes of matrices. The efficiency of the proposed technique was examined numerically, and the findings revealed a substantial enhancement over its previous modificationsItem Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach(Advances in Systems Sciences and Applications (ASSA), 2022-12-30) Oguntolu, Festus Abiodun; Peter, Olumuyiwa James; Oshinubi, Kayode; Ayoola, Tawakalt Abosede; Oladapo, Asimiyu Olalekan; Ojo, Mayowa MichaelTuberculosis (TB) is an infectious disease caused by mycobacterium disease which causes major ill health in humans. Control strategies like vaccines, early detention, treatment and isolation are required to minimize or eradicate this deadly pandemic disease. This article presents a novel mathematical modelling approach to tuberculosis disease using Vaccinated-Susceptible-Latent-Mild-Chronic-Isolated-Treated model. We examined if the epidemiology model is well posed and then obtained two equilibria points (disease free and endemic equilibrium). We also showed that TB disease free equilibrium is locally and globally asymptotically stable if . We solved the model analytically using Homotopy Perturbation Method (HPM) and the graphical representations and interpretations of various effects of the model parameters in order to measure the impact for effective disease control are presented. The findings show that infected populations will be reduced when the isolation and treatment rates and their effectiveness are high.Item Analytical Study of Viscous Fluid Movement in a Rectangular Pipe using Diffusion Magnetic Resonance Equation(Nigerian Journal of Theoretical and Environmental Physics, 2024-09) Yusuf S. I.Silicene, a two-dimensional material analogous to graphene, has garnered Diffusion Magnetic Resonance Imaging (DMRI) equation is used in this research work to examine the flow of fluid in a rectangular. Having previously considered flow in cylindrical and spherical coordinates, this study explores the rectangular channel of a three dimensional - (3D) flow using DMRI equation evolved and solved analytically using the method of separation of variables (MSV) with appropriate boundary conditions applied. Relaxation times of three viscous fluids were used - crude oil, oil wax and black oil in the simulation and the values of magnetization registered by each fluid recorded. The results obtained showed that oil wax has the highest value of magnetization followed by crude oil and then black oil. The study underscores the multivarious ways diffusion MRI can be applied and its use in the analysis of flow of viscous fluid through different geometrical channels.Item Annual Effective Dose Estimation due to Gross Alpha and Beta Activities in Nigerian Bottled Drinking Water(2020) Kolo, M. T.,; OLARINOYE, OYELEKE; SANUSI E; AJAYI M; KADIR A; UMAR S.I; AYEDUN FBackground: Extremely humid, hot and dry climatic conditions of Nigeria has led to an increasing demand for clear and clean portable water supply across the nation. Additionally, the dehydrating traffic situations commonly witnessed in virtually all the major cities in Nigeria has made consumption of bottled water indispensable component of modern life in Nigeria. It is therefore important that the radiological burden incurred by the Nigerian population from ingestion of bottled water be investigated. Materials and Method: Twenty one brands of commercial bottled water regularly consumed in Nigeria were obtained from standard supermarkets and investigated for their gross alpha and gross beta radioactivity. This analysis, as a recommended first step in radio analytical screening, was performed using a gas-free, low background dual phosphor proportional counter. Results: Results of the analysis showed that mean values for gross alpha and gross beta activity concentrations in all the investigated bottled water samples were 15.22±0.93 mBq l-1 and 39.69±1.83 mBq l-1 respectively. These values were below safety limits recommended by the World Health organization. Computed average annual effective dose equivalent for adults, children and infants (lactating age) in Nigeria due to consumption of commercial bottled water were lower than the recommended safeguard of 0.1 mSv for drinking water. Conclusion: The results does not suggest any radiological threat to the health of consumers. However, intermittent monitoring of commercially consumed bottled water is recommended for water quality compliance from radiation safety perspective.Item Application of Adomian Decomposition Method (ADM) for solving Mathematical Model of Measles(National Mathematical Center, 2021-03-22) Abdurrahman, Nurat Olamide; Somma S. A.; Ayegbusi F. D.; Gana P.; Adama P. W.; Yisa E. M.Item Application of Aeromagnetic Data to Assess the Structures and Solid Mineral Potentials in Part of North Central Nigeria(Journal of Geography, Environment and Earth Science International, 2020) ADETONA, Adebayo Abbass. 15. M.D. Tawey, D.U. AlhassanAssessment of the structures and solid minerals was carryout to investigate subsurface structural characteristics and mineralization potential zones within part of north-central Nigeria. The residual magnetic intensity data of the area was reduced to magnetic pole after which several source edge detection/interpretation with depth determination techniques including, analytic signal; tilt derivative; first and second vertical derivatives and Euler deconvolution were applied to the aeromagnetic data. From the analytic signal map, three magnetic zones were delineated. These are: low to relatively low magnetic zone (LM) with amplitude range from 0.003 to 0.009, moderate magnetic zone (MM) with amplitude 0.009 to 0.106 and those with amplitudes above 0.106 were products of later magmatic intrusions into host with fractures, faults and joints. Tilt derivative helped in delineating location and extent of edges of causative sources while Euler deconvolution helps in determination of boundary, depth and geometry of the structures. From first vertical derivative mapstructures were found to have high lineament density around the central portion of the area and span toward the western end of the map were delineated. The lineaments mapped trending in the ENE-WSW followed by WNW-ESE with some NE-SW, NNE-SSW and NNW-SSE trends. The second vertical derivative (SVD) map also helped in delineating structures and possible mineralization zones that are pronounced within the study area, around high analytic signal zones. Delineated possible and favorable mineralization zones from second vertical derivative map correlate with portion of the study area with rocks showing high analytic signal amplitude suggesting the rocks to be of later magmatic intrusions where mineralization fluids solidify within the host rocks.Item Application of Grey-Markov Model for Forecasting Nigeria Annual Rice Production(African Journal Online (AJOL), South Africa, 2021-11-21) Lawal Adamu; Didigwu, N. E.; Saidu, D. Y; Sadiq, S. L.; Khadeejah James AuduIn this paper, Grey system model (GM(1,1)) and Grey-Markov model that forecast Nigeria annual Rice production have been presented. The data used in the research were collected from the archive of Central Bank of Nigeria for a period of Six years (2010-2015). The fitted models showed high level of accuracy. Hence, the models can be used for food security plans of the nation.Item Application of Hidden Markov Model in Yam Yield Forecasting.(African Journal Online (AJOL), Soutrh Africa, 2022-06-06) 11. Lawal Adamu; Saidu Daudu Yakubu; Didigwu Ndidiamaka Edith; Abdullahi Abubakar; Khadeejah James Audu; Isaac Adaji.Providing the government and farmers with reliable and dependable information about crop yields before each growing season begins is the thrust of this research. A four-state stochastic model was formulated using the principle of Markov, each state of the model has three possible observations. The model is designed to make a forecast of yam yield in the next and subsequent growing seasons given the yam yield in the present growing season. The parameters of the model were estimated from the yam yield data of Niger state, Nigeria for the period of sixteen years(2001-2016). After which, the model was trained using Baum-Welch algorithm to attend maximum likelihood. A short time validity test conduct on the model showed good performance. Both the validity test and the future forecast shows prevalence of High yam yield, this attest to the reality on the ground, that Niger State is one of the largest producers of yam in Nigeria. The general performance of the model, showed that it is reliable therefore, the results from the model could serve as a guide to the yam farmers and the government to plan strategies for high yam production in the region.Item Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM).(Pacific Journal of Science and Technology, 2013-11-20) 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 Approximate Solution of Typhoid Fever Model by Variational Iteration Method(ATBU, Journal of Science, Technology & Education (JOSTE), 2018-09) A. F. Adebisi; O. J. Peter; T. A. Ayoola; F. A. Oguntolu; C. Y. IsholaIn this paper, a deterministic mathematical model involving the transmission dynamics of typhoid fever is presented and studied. Basic idea of the disease transmission using compartmental modeling is discussed. The aim of this paper is to apply Variational Iteration Method (VIM) to solve typhoid fever model for a given constant population. This mathematical model is described by nonlinear first order ordinary differential equations. First, we find the solution of the model by using Variation Iteration Method (VIM). The validity of the VIM in solving the model is established by classical fourth-order Runge-Kutta method (RK4) implemented in Maple 18. In order to show the efficiency of the method we compare the solutions obtained by VIM and RK4. We illustrated the profiles of the solutions of each of the compartments, from which we speculate that the VIM and RK4 solutions agreed well.