A Block Procedure with Continuous Coefficients for the Direct Solution of General Second Order Initial Value Problems of (Odes) Using Shifted Legendre Polynomials as Basis Function

Abstract

This paper presents a self starting block method for the direct solution of general second order initial value problems of ordinary differential equations. The method was developed via interpolation and collocation of the shifted Legendre polynomial as basis function. A continuous linear multistep method was generated and was evaluated at some desired points to give the discrete block method. The block method was investigated and was found to be consistent, zero stable and convergent. The method was applied on some nonlinear as well as linear ordinary differential equations problems and the performance was relatively better than those constructed by [1], [12] and [15] respectively.