AN ORTHOGONAL POLYNOMIAL AS A BASIS FUNCTION FOR THE FORMULATION OF HYBRID METHODS FOR FIRST ORDER INITIAL VALUE PROBLEM

Abstract

 A class of orthogonal polynomial was constructed in the interval [0, 1], with weight function w(x) = 1 - x which was employed as a basis function of the approximant to the solution of first Order ordinary differential equation, for generating the required numerical scheme through collocation and interpolation approach. Some classes of continuous linear multistep method for the solution of the problem were derived. The resulting scheme were implemented on some examples, the result show that the method is effective.