A Block Hybrid Method for the Direct Solution of y^(”)=f(x,y,y^(’))

This paper introduces a Block Hybrid Method for solving general second-order ordinary differential equations (ODEs) with initial value problems. The method is based on a continuous formulation of the second-order hybrid generalized Adams method, incorporating one off-grid point per step. Discrete schemes are derived from the continuous form and its first derivative, forming the block methods. Analysis shows the method is consistent, zero-stable, and convergent. Numerical results highlight its superiority over existing methods.