Asian Journal of Pure and Applied Mathematics

The new Trigonometric-Fitted One-Step Three Points Hybrid Block Method presented in this study is designed to handle the difficulties posed by stiff and oscillatory differential equations. Using the collocation of the trigonometrically function as the basis function and the interpolation approach, the continuous hybrid methodology was developed. After instilling the transformation method to create a continuous block method, it was assessed at non-interpolating places. Upon evaluating the continuous block at every stage, the discrete block method was restored. The basic properties of the methods were found to be convergent, consistent, and zero-stable after research. A few problems involving stiff and oscillatory ordinary differential equations are solved using the new approach. Comparing the numerical results of the developed methods, it was discovered that our method outperforms the current method mentioned in the reference in terms of approximation.