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All Journal African Multidisciplinary Journal of Sciences and Artificial Intelligence
Olalekan Femi Famutimi
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology

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A New Numerical Scheme for Solving Quadratic Riccati Differential Equations (QRDEs) Ezekiel Olaoluwa Omole; Adefunke Bosede Familua; Lawrence Osa Adoghe; Oyindamola Racheal Oyebanjo; Rasaki Yinka Akinbo; Olalekan Femi Famutimi
African Multidisciplinary Journal of Sciences and Artificial Intelligence Vol 3 No 1 (2026): African Multidisciplinary Journal of Sciences and Artificial Intelligence
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/amjsai.v3i1.9362

Abstract

Quadratic Riccati Differential Equations (QRDEs) are important in control theory, optimal stabilization, and nonlinear dynamics, thereby requiring numerical methods that are both accurate and computationally reliable. This study introduces a new numerical scheme (NNS) for solving QRDEs using an eighth-order power series basis function combined with interpolation and collocation techniques to approximate the exact solutions over a one-step integration interval. Through this procedure, the continuous differential equation is transformed into a system of nonlinear algebraic equations, which is then solved using the Gauss elimination method. A detailed analysis of the proposed scheme establishes its high order of accuracy, zero stability, consistency, convergence, and absolute stability, confirming its suitability for practical computation. The method was implemented on four different QRDE problems, and the results showed that the approximate solutions were in excellent agreement with the exact solutions throughout the integration interval. The study concludes that the proposed NNS is a robust, accurate, and broadly applicable approach for the numerical solution of QRDEs, offering a reliable contribution to computational methods for nonlinear differential equations.
Co-Authors Adefunke Bosede Familua Ezekiel Olaoluwa Omole Lawrence Osa Adoghe Oyindamola Racheal Oyebanjo Rasaki Yinka Akinbo