Six Points Implicit Block Method with Extra Derivative for Solving Second Order Ordinary Differential Equations

The construction of the six-point block methods with extra derivatives for solving directly is presented in this paper. The suggested block methods concurrently approximate the problem's solution at six points and are formulated using the Hermite Interpolating Polynomial. The block methods do not reduce the equation to a first-order system of initial value problems (IVPs); instead, they directly obtain the numerical solutions. Additionally, the order and zero-stability of the suggested techniques are examined. We present numerical results and draw comparisons with other block methods that are currently in use. The results demonstrate how effective the suggested approaches are at solving second-order IVPs in general.