Browsing by Author "Ayinde, A.M"

Now showing 1 - 3 of 3
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    A Novel Block Method for Direct Simulation of Higher-Order Oscillatory Differential Equations Using Power Series Polynomials
    (Faculty of Physical Sciences, University of Ilorin, 2026) Bello , K. A; Raji , M. T.; Ishaq , A. A; Ayinde, A.M
    This study introduces a novel block method for the direct numerical integration of higher-order oscillatory differential equations. The method employs power series polynomials as basis function within a collocation and interpolation framework. The effectiveness of the proposed approach is demonstrated through its application to second and third-order oscillatory test problems, including the classical mass-spring system. A rigorous theoretical analysis confirms that the method is consistent, zero-stable, and convergent, achieving a uniform order of five. Linear stability analysis reveals a substantial region of absolute stability, indicating its suitability for mildly stiff problems. Numerical results, presented in tables and figures, show that the proposed method achieves significantly higher accuracy and faster convergence compared to existing techniques. This affirms the reliability and efficacy of the technique for the direct simulation of higher-order oscillatory differential equations.
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    Analysis of Convergence of Block Methods in Simulating Epidemic Diseases
    (The Faculty of Natural and Applied Sciences, Ignatius Ajuru University of Education, Rumuolumeni,River states, Nigeria., 2024) Bello, K.A; James, A.A; Ayinde, A.M; Sabo, J
    This research delves into a comprehensive examination of the application and convergence analysis of a newly developed block method for simulating epidemic models. The focal point of this study revolves around the derivation and implementation of a novel scheme, crafted through the utilization of power series polynomials, ensuring the fulfilment of essential properties. The formulation of the new scheme was rooted in the power series polynomial, a mathematical construct known for its versatility and precision. The rigorous validation process confirmed that the derived scheme satisfied the requisite properties, thereby establishing its theoretical soundness. The crux of the investigation lies in the practical application of this innovative scheme to simulate an epidemic model. Through meticulous simulations, the results yielded compelling evidence of the new method's superiority over existing approaches considered in this research. The comparative analysis demonstrated a notable enhancement in both accuracy and convergence speed, highlighting the efficacy of the newly proposed scheme in capturing and predicting the dynamics of epidemics. The observed advantages of the new scheme are particularly noteworthy, showcasing its potential to revolutionize the field of epidemiological modelling. By outperforming established methods, the new approach not only contributes to the theoretical underpinnings of epidemic modelling but also holds significant promise for practical applications, such as forecasting disease spread and optimizing intervention strategies
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    Approximate Solution of An Ordinary Differential And Integral Equations Using Collocation Method Based On Hermite Legendre Polynomials
    (Faculty of Natural and Applied Sciences, Umaru Musa yar'adua University, Kastina, 2021-03) Ayinde, A.M; Aliyu, H.B; Bello, K.A; Adenipekun, A.E
    In this work, we employed an approximate solution of second and third-order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) by utilizing a standard collocation method based on Hermite and Legendre polynomials. The ODEs were first converted to integral equations and the basis function was substituted to obtain a set of linear algebraic which then form equations that were solved via maple 2021. Comparisons were made with the two trial solutions mentioned above in terms of errors obtained. Numerical examples were given to illustrate the performance of the method for various orders. However, the Hermite polynomial basis exhibits better accuracy over the Legendre polynomials in some results as can be seen from the tables of errors presented.