in this paper, we propose a modification of the second order method introduced in [q. li and x. y. wu, a two-step explicit $p$-stable method for solving second order initial value problems, textit{appl. math. comput.} {138} (2003), no. 2-3, 435--442] for the numerical solution of ivps for second order odes. the numerical results obtained by the new method for some...