Mathematics
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Item An Accelerated Iterative Technique: Third Refinement of Gauss-Seidel Algorithm for Linear Systems(MDPI, 2023-05-01)This study presents a novel accelerated iterative method referred to as the Third Refinement of the Gauss-Seidel Algorithm (TRGS) for solving large-scale linear systems of equations. By integrating a three-level refinement strategy into the classical Gauss-Seidel method, the proposed technique significantly improves the convergence rate and computational efficiency. The method is rigorously analyzed for consistency, stability, and convergence, and is evaluated through numerical experiments on various benchmark problems. Results demonstrate that the TRGS algorithm outperforms both the traditional Gauss-Seidel and other refinement-based methods in terms of iteration count and solution accuracy. This advancement offers a valuable contribution to numerical linear algebra, particularly in scientific computing where fast and accurate solutions to linear systems are critical.Item Refinement of Triple Accelerated Over Relaxation (RTAOR) Method for Solution of Linear System(Nigeria Mathematical Sciences (NMS), 2021-04-21) Khaddejah James Audu; Yahaya, Y. A.; Adeboye, K. R; Abubakar, U. YIn this paper, a Refinement of Extended Accelerated Over-Relaxation (REAOR) iterative method for solving linear systems is presented. The method is designed to solve problems of partial differential equations that results into linear systems having coefficient matrices such as weak irreducible diagonally dominant matrix and 𝐿−matrix (or 𝑀−matrix). Sufficient criterion for convergence are examined and few numerical illustrations are considered to ascertain efficiency of the new method. Outcome of the numerical results reveals that the REAOR iterative method is more efficient when compared with Extended Accelerated Over-Relaxation iterative method in terms of computational time, level of accuracy and required number of iterations for convergenceItem Refinements of Some Iterative Methods for Solving Linear System of Equations(Nigerian Women in Mathematics (NWM), 2023-06-20) Khadeejah James Audu; James Nkereuwem EssienThe efficient and accurate solution of linear systems of equations is a fundamental problem in various scientific and engineering fields. In this study, we focus on the refinements of iterative methods for solving linear systems of equations (▁A k=▁b). The research proposes two methods namely, third refinement of Jacobi method (TRJ) and third refinement of Gauss-Seidel (TRGS) method, which minimizes the spectral radius of the iteration matrix significantly when compared to any of the initial refinements of Jacobi and Gauss-Seidel methods. The study explores ways to optimize their convergence behavior by incorporating refinement techniques and adaptive strategies. These refinements exploit the structural properties of the coefficient matrix to achieve faster convergence and improved solution accuracy. To evaluate the effectiveness of the proposed refinements, numerical examples were tested to see the efficiency of the proposed TRJ and TRGS on a diverse set of linear equations. We compare the convergence behavior, computational efficiency, and solution accuracy of the refined iterative methods against their traditional counterparts. The experimental results demonstrate significant improvements in terms of convergence rate and computational efficiency when compared to their initial refinements. The proposed refinements have the potential to contribute to the development of more efficient and reliable solvers for linear systems, benefiting various scientific and engineering applications.Item Numerical Solution of Parabolic Partial Differential Equations via Conjugate Gradient Technique(Nigeria Mathematical Science (NMS), 2023-06-19) Khadeejah James AuduParabolic partial differential equations (PPDEs) arise in many areas of science and engineering, including heat transfer, diffusion, and fluid dynamics. Analytical solutions to these PPDEs are often difficult or impossible to obtain, so numerical methods are needed to approximate the solution. In this research, we investigate the use of the conjugate gradient technique for numerically solving parabolic PDEs. The technique involves discretizing the PPDE with regard to both space and time. The parabolic partial differential equations are then transformed into systems of linear algebraic equations using the Crank-Nicholson centred difference approach. Then, these equations are solved to yield the unknown points in the grids, which are subsequently substituted into the assumed solution to obtain the required estimated solution, which is reported in tabular format. A comparison was made between the conjugate gradient solutions and those produced using the Jacobi preconditioned conjugate gradient technique in terms of the time required and rate of convergence at that point. Results indicate that conjugate gradient techniques are suitable for solving parabolic-type partial differential equations, with Jacobi-preconditioned conjugate gradient technique converging faster. This research has potential applications in various areas of science and engineering where parabolic PDEs ariseItem A Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Interactions Functions(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0R . Graphical simulations are presented using some demographic and epidemiological data.Item Stability Analysis for Mathematical Modeling of Dengue Fever Transmission and Control(Proceedings of International Conference on Contemporary Developments in Mathematical Sciences (ICCDMS), 2021-04-13) Aliyu, A. H.; Akinwande, N. I.; Somma, Samuel AbuDengue fever is one of the greatest health challenges in the present world. In this work, mathematical modeling of dengue fever transmission and control was formulated. The model considered the human population h N and the vector population m N which are further subdivided into six classes, susceptible human 𝑆, infected human 𝐼, temporary recovered human class 1 R , permanently recovered human class 2 R , susceptible mosquito 1 M , and infected mosquito class 2 M . The Disease Free Equilibrium (DFE) point was obtained and the basic Reproduction number 0 R was computed. The Disease Free Equilibrium (DFE) is locally and globally asymptotically stable when R0 1.Item A Note on Combustible Forest Material (CFM) of Wildland Fire Spread(Proceedings of 3rd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2021-10-28) Zhiri, A. B.; Olayiwola, R. O.; Somma, Samuel AabuIn this paper, a mathematical model for combustible forest material of a wildland fire is presented. The equations describing the fractional components of forest fire were carefully studied. The reaction before a forest can burn or before fire can spread must involves fuel, heat and oxygen. The coupled dimensionless equations describing the phenomenon have been decoupled using perturbation method and solved analytically using eigen function expansion technique. The results obtained were graphically discussed and analysed. The study revealed that varying Radiation number and Peclet energy number enhances volume fractions of dry organic substance and moisture while they reduced volume fraction of coke.Item 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 AuduThis 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.Item Linear Programming for Profit Maximization of Agricultural Stock(Maths Model Research Group, FUT, Minna, Nigeria, 2024-02-18) Jacob Rebeccal; Nyor Ngutor; Khadeejah James AuduThis 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.Item Numerical Solutions of Higher Order Differential Equations via New Iterative Method(Maths Model Research Group, FUT, Minna, Nigeria, 2024-02-18) Khadeejah James AuduHigher 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.