Numerical Two-Step Three Off-grid Hybrid Optimized Fourth derivative Methods for Solving fourth order Initial Value Problems Base on Volterra Integral Equation of the Second Kind

This article present A two-step three-off grid hybrid optimized fourth derivative methods for solving fourth order initial value problems base on volterra integral equation of the second kind, the method proposes a power series as the basis function for a selected three hybrid points which suitably optimizes one of the three off-grid points by equating 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 by treating the other two as a free parameter, the basic properties of the method was scrutinize and the develop method is apply to work out some fourth order initial value problems of ordinary differential equations and from the numerical results obtained, it is observed that our new methods gives better approximation than the existing method compared with our result.