An algebraic method to solve the radial Schrödinger equation

We propose a method of numerical integration of differential equations of the type x2y′′ + f (x)y = 0 by approximating its solution with solutions of equations of the type x2y′′ + (ax2+bx+c)y = 0. This approximation is performed by segmentary approximation on an interval. We apply the method to obtain approximate solutions of the radial Schrödinger equation on a given interval and test it for two different potentials. We conclude that our method gives a similar accuracy than the Taylor method of higher order.