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

Document Type : Research Paper


Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran


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 problems show its superiority in efficiency‎,
‎accuracy and stability‎.‎‎


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