Browsing by Author "Yahaya Yusuph Amuda"

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    Advancements in Solving Higher-Order Ordinary Differential Equations via the Variational Iterative Method.
    (Akdeniz University, Turkey, 2025-12-30) Khadeejah James Audu; Michael Ogbole Ogwuche; Sıkırulaı Abolaji Akande; Yahaya Yusuph Amuda
    This study presents advancements in solving higher-order ordinary differential equations (ODEs) using the Variational Iterative Method (VIM) and compares its performance with the New Iteration Method (NIM) and Adomian Decomposition Method (ADM). ODEs are critical in modeling the rate of change in various systems over time, and many do not have exact solutions, necessitating the use of numerical methods to obtain approximate results. While several iterative methods exist, a detailed comparison of VIM with other techniques, particularly for higher-order ODEs, is still lacking. This research focuses on understanding the principles and methodology of VIM and applying it to solve higher-order linear and nonlinear ODEs. The study evaluates the accuracy, convergence rate, and computational efficiency of VIM compared to NIM and ADM through the solution of third, fourth, and fifth-order differential problems. The results show that VIM outperforms NIM and ADM, with faster convergence and higher efficiency. Error analysis in Figures 1, 2, and 3 highlights the strengths and limitations of each method, providing valuable insights for researchers and practitioners in selecting the most appropriate technique for solving higher-order ODEs. These findings advance the development of iterative methods in numerical analysis and contribute to progress in the field of differential equations.
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    Comparative Numerical Evaluation of Some Runge-Kutta Methods for Solving First Order Systems of ODEs
    (Toros University Publishing house, Turkey, 2025-12-12) Khadeejah James Audu; Tunde Adekunle Abubakar; Yahaya Yusuph Amuda; James Essien Nkereuwem
    In this study, a comparative analysis of two Runge-Kutta methods; fourth-order Runge-Kutta method and Butcher’s Fifth Order Runge-Kutta method are presented and used to solve systems of first-order linear Ordinary Differential Equations (ODEs). The main interest of this work is to test the accuracy, convergence rate and computational efficiency of these methods by using different numerical problems of ODEs. Empirical conclusions are drawn after close observation of the results presented by the two methods, which further highlights their limitations and enabling researchers to make informed decisions in choosing the appropriate technique for specific systems of ODEs problems.