The symmetric two-step P-stable nonlinear predictor-corrector‎ ‎methods for the numerical solution of second order‎ ‎initial value problems

Abstract

In this paper‎, ‎we propose a modification of the second order method‎ <br />‎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, <br />‎435--442‎] for the numerical solution of‎ <br />‎IVPs for second order ODEs‎. ‎The numerical results obtained by the‎ <br />‎new method for some problems show its superiority in efficiency‎, <br />‎accuracy and stability‎.‎‎