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All Journal African Multidisciplinary Journal of Sciences and Artificial Intelligence
Adedokun Opeyemi Benjamin
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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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Trigonometric-Fitted One-Step 3 Points Hybrid Block Method for the Solution of Stiff and Oscillating Problems Raymond Dominic; Adedokun Opeyemi Benjamin; Olanrewaju Philip Oladapo
African Multidisciplinary Journal of Sciences and Artificial Intelligence Vol 1 No 1 (2024): 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.v1i1.3551

Abstract

This paper introduces a novel Trigonometric-Fitted One-Step 3 Points Hybrid Block Method tailored for addressing the complexities associated with stiff and oscillating differential equations.The continuous hybrid technique was created using the interpolation method and the collocation of the trigonometrical function as the basis function. It was then eval_uated at non-interpolating points by inculcating the transformation method to produce a continuous block method. When the continuous block was assessed at each stage, the discrete block approach was regained. Upon investigation, the fundamental characteristics of the techniques were discovered to be zero-stable, consistent, and convergent. The new method is used to solve a few stiff and oscillatory ordinary differential equation problems. Comparisons of numerical results of the derived methods, it was found that our approach provides a better approximation than the existing method cited in the reference. AMS subject classification: 65L05, 65L06, 65L20
Co-Authors Olanrewaju Philip Oladapo Raymond Dominic