A New Numerical Algorithm for the Solution of General Second Order Ordinary Differential Equations

This paper contains the formulation of an algorithm for solving general second order initial value problems of ordinary differential equations. This method is basically a continuous linear multistep (clmm) block method obtained from the collocation and interpo lation of a functional as basis function. Its implementation was on the evaluation of the main method and two additional methods of the block matrix. It is proved that the algorithm is consistent, zero-stable and convergent. Errors obtained using uniform step lengths were also investigated and presented Numerical examples are provided to show the efficiency and suitability of the algorithm.