Modifed Finite Integration Method by Using Legendre Polynomials for Solving Linear Ordinary Diﬀerential Equations
In this paper, we construct a numerical procedure which is called the finite integration method by using the Legendre polynomial. This numerical procedure is for solving the linear ordinary diﬀerential equations. That is, we define the solution as a linear combination of the Legendre polynomials and we use the zeros of Legendre polynomial as computational grid points. We implement this procedure with several numerical examples to demonstrate the accuracy of our method comparing to the finite diﬀerence method, the traditional finite integration methods and their analytical solutions.