Solving second order non-linear boundary value problems by four numerical methods

Abstract EN

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.

Keywords: Boundary value problem, Rung-Kutta RK4, Rung–Kutta Butcher, Differential transformation method, Homotopy perturbation method.