A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

In this paper, a new kind of analytical method of nonlinear problem called the process analysis method (PAM) is described and used to give a second-order approximate solution of a simple pendulum. The PAM does not depend on the small parameter supposition and therefore can overcome the disadvantages and limitations of the perturbation expansion method. The analytical approximate results at the second-order of approximation are in good agreement with the numerical results. They are compared with perturbation solutions, and it appears that even the first-order solutions are more accurate than the perturbation solutions at second-order of approximation.