University of KashanIranian Journal of Mathematical Chemistry2228-648911120200301A New Explicit Singularly P-Stable Four-Step Method for the Numerical Solution of Second Order IVPs173110531610.22052/ijmc.2020.207671.1472ENMohammadMehdizadeh KhalsaraeiDepartment of mathematics, University of Maragheh, Amirkabir Highway, P. O. Box. 55181-83111AliShokriDepartment of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.0000-0003-2699-1490Journal Article20191105In this paper, we introduce a new symmetric explicit four-step method with variable coefficients for the numerical solution of second-order linear periodic and oscillatory initial value problems of ordinary differential equations. For the first time in the literature, we generate an explicit method with the most important singularly P-stability property. The method is multiderivative and has algebraic order eight and infinite order of phase-lag. The numerical results for some chemical (e.g. orbit problems of Stiefel and Bettis) as well as quantum chemistry problems (i.e. systems of coupled differential equations) indicated that the new method is superior, efficient, accurate and stable.https://ijmc.kashanu.ac.ir/article_105316_cf6ff6111c1398417f28d801c2cf3b23.pdf