Orthogonal-Based Second Order Hybrid Initial Value Problem Solver

This work focuses on development of an initial value problem solver by employing a new class of orthogonal polynomial, the basis function. We present the recursive formula of the class of polynomials constructed and adopt collocation technique to develop the method. The method was analyzed for its basic properties and findings show that the method is accurate and convergent.AMS Subject Classification: 65L05, 65L06 Keywords: Orthogonal polynomials, Algorithm, Block method, Collocation, Interpolation, Zero-Stable.