School of Physical Sciences (SPS)
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School of Physical Sciences (SPS)
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Item 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 An Investigative Comparison of Higher-Order Runge-Kutta Techniques for Resolving First-Order Differential Equations(Fırat University, Turkey, 2025-07-14) Khadeejah James Audu; Victor James Udoh; Jamiu GarbaIn the context of solving first-order ordinary differential equations (ODEs), this paper thoroughly compares various higher-order Runge-Kutta methods. Reviewing the effectiveness, precision, and practicality of several Runge-Kutta schemes and highlighting their usage in numerical approximation is the main goal of the research. The study explores traditional approaches, including the fifth-order, six-stage Runge-Kutta (RK56), the sixth-order, seven-stage Runge-Kutta (RK67), and the seventh-order, nine-stage Runge-Kutta (RK79), with the goal of offering a comprehensive comprehension of their individual advantages and disadvantages. In order to help academics and practitioners choose the best approach based on the features of the problem, comparative benchmarks are constructed, utilizing both theoretical underpinnings and real-world implementations. Robustness evaluations and sensitivity analysis complement the comparison research by illuminating how flexible these techniques are in various context. The results of this study provide important new understandings of how higherorder Runge-Kutta methods function and provide a thorough manual for applying them to solve first-order differential problems in a variety of scientific and engineering fields. The study’s examination of three higher order Runge-Kutta algorithms reveals that the RK56 is more effective at solving first order ODEsItem Application of Backward Differentiation Formula on Fourth-Order Differential Equations.(Universiti Tun Hussein Onn Malaysia Publisher’s Office, Malaysia, 2022-12-30) Khadeejah James Audu; Jamiu Garba; Abdgafar Tunde Tiamiyu; Blessing Ashiodime ThomasHigher order ordinary differential equations are typically encountered in engineering, physical science, biological sciences, and numerous other fields. The analytical solution of the majority of engineering problems involving higher-order ordinary differential equations is not a simple task. Various numerical techniques have been proposed for higher-order initial value problems (IVP), but a higher degree of precision is still required. In this paper, we propose a novel two-step backward differentiation formula in the class of linear multistep schemes with a higher order of accuracy for solving ordinary differential equations of the fourth order. The proposed method was created by combining interpolation and collocation techniques with the use of power series as the basis function at some grid and off-grid locations to generate a hybrid continuous two-step technique. The method's fundamental properties, such as order, zero stability, error constant, consistency, and convergence, were explored, and the analysis showed that it is zero stable, consistent and convergent. The developed method is suitable for numerically integrating linear and nonlinear differential equations of the fourth order. Four Numerical tests are presented to demonstrate the efficiency and accuracy of the proposed scheme in comparison to some existing block methods. Based on what has been observed, the numerical results indicate that the proposed scheme is a superior method for estimating fourth-order problems than the method previously employed, confirming its convergence.Item Extended accelerated overrelaxation iteration techniques in solving heat distribution problems(Price of Songkla University, Thailand, 2023-10-05) Khadeejah James AuduSeveral stationary iteration techniques for numerical solutions to special systems of linear equation systems of the form 𝒜𝑢 = 𝑏 have been studied in an attempt to improve their convergence, suitability, and strength. Among such techniques is the Extended Accelerated Overrelaxation (EAOR) iterative scheme. In this paper, we studied the basics of the EAOR methods and applied them to compute the solution of a real-life problem, resolving the heat equation when a steady temperature is applied to a metal plate. We show how the real-life problem can be modeled into a partial differential equation, followed by discretization through the use of finite differences, and finally generating a largely sparse system of algebraic linear equations, from which the unknowns are to be solved. The techniques were compared with the Refinement of Accelerated Overrelaxation (RAOR) iterative scheme. The outcome of the numerical tests proves the effectiveness of the EAOR schemes for such problems.Item Effects of Relaxation Times from Bloch Equations on Age-Related Change in White and Grey Matter(University of Lagos, Nigeria, 2024-02-20) Yusuf, S. I.; D. O. Olaoye; M. O. Dada; A. Saba; Khadeejah James Audu; J. A. Ibrahim; A. O. JattoThis research work presented the analytical method of using T1 and T2 relaxation rates of white matter and grey matter to distinguish the passage of time on human organs. A time dependent model equation evolved from the Bloch Nuclear Magnetic Resonance equation was solved under the influence of the radio frequency magnetic field [rfB1(x, t) ̸= 0] and in the absence of radio frequency magnetic field [rfB1(x, t) = 0]. The general solution was considered in three cases. Analysis of the solutions obtained revealed that the rate of decrease of the white matter was faster than that of the grey matter. Between 100 and 400 seconds the difference is more noticeable.Item Refinement of Extended Accelerated Over Relaxation method for solution of linear systems.(Benue State University, Makurdi, Nigeria, 2021-09-22) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.Given any linear stationary iterative methods in the form 𝑧(𝑖+1) = 𝐽𝑧(𝑖) + 𝑓, where 𝐽 is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form 𝐴𝑧 = 𝑏. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.Item Yusuf, S. I., Abdulsalam T.O., Audu, K. J., Jatto, A. O. and Ibrahim J. A (2022). Investigation of Dispersal Rate of Curry and Thyme. Journal of Science, Technology, Mathematics and Education, 18(3), 223-229.(Federal University of Technology, Minna, Nigeria, 2022-09-22) Yusuf, S. I.; Abdulsalam T.O.; Khadeejah James Audu; Jatto, A. O.; Ibrahim J.This is a study of the rate of dispersal of curry and thyme in a medium using the coefficient of diffusion of curry leaves and thyme leaves. The study was carried out by solving the diffusion equation using the method of separation of variables with appropriate boundary conditions and the coefficient of diffusion applied for curry and thyme. The result shows that curry leaves diffuse faster than thyme leaves under the same conditions. The research establishes why nutritionists and cooks would choose curry ahead of thyme when considering appropriate spices for cooking in order to attract attention.Item Analysis of Fire Outbreak in Coupled Atmospheric-Wildfire.(Ibrahim Badamasi Babangida University, Lapai, Nigeria, 2021-06-20) Zhiri, A. B.; Olayiwola, R. O.; Khadeejah James Audu; Adeloye, T. O.; Gupa, M. IForest fire outbreak has become alarming day by day as it is a common occurrence in most parts of the world and it cause a lot of havoc to biodiversity as well as to the local ecology. In this paper, a partial differential equations (PDE) governing wildland fire outbreak is presented. We obtained the approximate analytical solution of the model using perturbation method, direct integration and eigenfunction expansion technique, which clearly depicts the influence of the parameters involved in the system. The effect of change in parameters such as Radiation number, Peclet energy number, Peclet mass number, and Equilibrium wind velocity on oxygen concentration are shown graphically and discussed. The results obtained revealed that as Radiation number and Peclet energy number increases, oxygen concentration depreciates. While increasing Peclet mass number, and Equilibrium wind velocity enhanced oxygen concentration.Item EXTENDED ACCELERATED OVER-RELAXATION (EAOR) METHOD FOR SOLUTION OF A LARGE AND SPARSELINEAR SYSTEMS(Federal University of Technology, Minna, Nigeria, 2021-06-14) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.In this research, we introduce a stationary iterative method called Extended Accelerated Over Relaxation (EAOR) method for solving linear systems. The method, an extension of the Accelerated Over Relaxation (A OR) method, was derived through the interpolation procedure with respect to the sub-matrices in application of a genera/ linear stationary schemes. We studied the convergence properties of the method for special matrices such as L-, H- and irreducible diagonally dominant matrices and proposed some convergence theorems. Some numerical tests were carried out to test the efficiency of the proposed method with existing methods in terms of number of iterations, spectral radius and computational time. The results revealed the superiority of the proposed EAOR method over the AOR method in terms of convergence rate.