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

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