%0 Journal Article
%T A New Explicit Singularly P-Stable Four-Step Method for the Numerical Solution of Second Order IVPs
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Mehdizadeh Khalsaraei, Mohammad
%A Shokri, Ali
%D 2020
%\ 03/01/2020
%V 11
%N 1
%P 17-31
%! A New Explicit Singularly P-Stable Four-Step Method for the Numerical Solution of Second Order IVPs
%K Explicit methods
%K Phase-lag
%K Ordinary differential equations
%K P-stable
%K Symmetric multistep methods
%R 10.22052/ijmc.2020.207671.1472
%X In 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.
%U http://ijmc.kashanu.ac.ir/article_105316_cf6ff6111c1398417f28d801c2cf3b23.pdf