Browsing by Author "Jamiu Garba"

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    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 Garba
    In 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 ODEs
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    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 Thomas
    Higher 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.