Three-Step Exponentially Fitted Two Hybrid Optimized Points for the Solution of Fourth Order Ordinary Differential Equations (ODEs)

This article presents an exponential fitted optimized three-step, two-off-grid hybrid point for the solution of fourth order ordinary differential equations. The method uses an exponential function as the basis function for a chosen two hybrid points, appropriately optimizing one of the two off-grid points by setting the principal term of the local truncation error to zero and using the local truncation error to determine the approximate values of the unknown parameter. Basic properties were examined, and the developed method was experimented to work out some fourth order initial value problems of ordinary differential equations. From the numerical results, it is clear that our new approach provides a better approximation than the existing method when compared to our result.