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 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 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 Application of Singular Value Decomposition technique for compressing images(Bauchi State University, Gadau, Nigeria, 2022-08-19) Khadeejah James AuduImage processing is becoming increasingly important as imaging technology has advanced. A storage constraint might occur even when image quality is an influential factor. This means finding a way to reduce the volume of data while still retaining quality, since compactable systems and minimal space are more desirable in the current computing field. An image compression technique that is frequently used is singular value decomposition (SVD). SVD is a challenging and promising way to loosely compress images, given how many people use images now and how many different kinds of media there are. SVD can be employed to compress digital images by approximating the matrices that generate such images, thereby saving memory while quality is affected negligibly. The technique is a great tool for lowering image dimensions. However, SVD on a large dataset might be expensive and time-consuming. The current study focuses on its improvement and implements the proposed technique in a Python environment. We illustrate the concept of SVD, apply its technique to compress an image through the use of an improved SVD process, and further compare it with some existing techniques. The proposed technique was used to test and evaluate the compression of images under various r-terms, and the singular value characteristics were incorporated into image processing. By utilization of the proposed SVD technique, it was possible to compress a large image of dimension 4928 x 3264 pixels into a reduced 342 x 231 pixels with fair quality. The result has led to better image compression in terms of size, processing time, and errors.Item 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 realms