Fourth Derivative Methods for Solving Fourth-Order Initial Value Problems Using an Optimized Three-Step, Two-Off Grid

In order to solve fourth-order ordinary differential equations, this article presents an optimized three-step, two-off-grid hybrid point fourth derivative method.The method uses an exponential function as the basis function for a chosen three 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.The method's basic properties were examined, and the developed method was applied to work out some fourth order initial value problems of ordinary differential equations.Based on the numerical results, it is observed that our new approach provides a better approximation than the existing method when compared to our result.