The boundary value problems for the 2nd order non-linear ordinary
differential equations are solved by using four numerical methods. These
numerical methods are Rung-Kutta of 4th order, Rung–Kutta Butcher of 6th order,
differential transformation method, and the Homotopy perturbation method. Three
physical problems from the literature are solved by the four methods for comparing
the results. The results were presented in tables and figures. The differential
transformation method appeared to be effective and reliable to find the semi
numerical-analytical solutions for such type of boundary value problems.