Exponentially-Fitted One-Step Four Hybrid Point Methods for Solving Stiff and Oscillating Problems

The one-step, four hybrid point approach for solving second-order stiff and oscillatory differential equations is presented in this study. The continuous hybrid technique was created using the interpolation method and the collocation of the exponential function as the basis function. It was then evaluated at non-interpolating points 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. Based on the numerical results, it was found that our approach provides a better approximation than the current method.