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 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 A COMPARATIVE ANALYSIS OF TWO SEMI ANALYTIC APPROACHES IN SOLVING SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS(Mehmet Akif Ersoy University, Turkey., 2024-06-29) Khadeejah James Audu; Onifade BabatundeThe resolution of systems of first-order ordinary differential equations (ODEs) is a critical endeavor with extensive applications in various scientific and engineering fields. This study presents a rigorous comparative assessment of two semi-analytic methodologies: the Variational Iterative Method (VIM) and the New Iterative Method (NIM). Addressing a significant research gap, our investigation explores the relative merits and demerits of these approaches. We provide a comprehensive examination of VIM, a well-established method, alongside NIM, a relatively less explored approach, to identify their comparative strengths and limitations. Furthermore, the study enriches existing knowledge in numerical methods for ODEs by highlighting essential performance characteristics such as convergence properties, computational efficiency, and accuracy across a diverse array of ODE systems. Through meticulous numerical experimentation, we uncover practical insights into the efficacy of VIM and NIM, bridging a critical knowledge gap in the field of numerical ODE solvers. Our findings demonstrate VIM as the more effective method, thereby enhancing the understanding of semi-analytic approaches for solving ODE systems and providing valuable guidance for practitioners and researchers in selecting the most appropriate method for their specific applicationsItem Enhancing Linear System Solving Through Third Refinement of Successive and Accelerated Over-Relaxation Methods(Çankaya University, Turkey, 2024-03-27) Khadeejah James Audu; Malik Oniwinde Oyetunji; James Essien NkereuwemOne of the primary difficulties in linear algebra, considering its widespread application in many different domains, is solving linear system of equations. It is nevertheless apparent that there is a need for a quick, effective approach that can handle a variety of linear systems. In the realm of large and sparse systems, iterative methods play a crucial role in finding solutions. This research paper makes a significant contribution by introducing an enhancement to the current methodology Successive and Accelerated Over Relaxation methods, referred to as the "Third Refinement of Successive and Accelerated Over Relaxation Methods." This new iterative approach demonstrates its effectiveness when applied to coefficient matrices exhibiting properties such as 𝑀- matrix, irreducible diagonal dominance, positive definiteness and symmetry characteristics. Significantly, the proposed method substantially reduces the spectral radius, resulting in fewer iterations and notably enhancing the convergence rate. Numerical experiments were conducted to evaluate its performance compared to existing second refinement of Successive and Accelerated Over Relaxation methods. The outcomes underscore the "Third Refinement of Successive and Accelerated Over Relaxation" methods potentially to boost the efficiency of solving linear systems, thus rendering it a valuable asset within the arsenal of numerical methodologies utilized in scientific and engineering realmsItem Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations(Penteract Technology, Malaysia, 2024-06-16) Khadeejah James Audu; Marshal Benjamin; Umaru Mohammed; Yusuph Amuda YahayaOrdinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)- based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.Item Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations(Malaysian Journal of Science and Advanced Technology, 2024-05-28) Khadeejah James Audu; Marshal Benjamin; Umaru Mohammed; Yusuph Amuda YahayaOrdinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)- based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.