A Generalized Family of Symmetric Multistep Methods with Minimal Phase-Lag for Initial Value Problems in Ordinary Differential Equations

Abstract

In the present paper, we formulate a generalized family of symmetric multistep methods (GFSMMs) for solving initial value problems in ordinary differential equations. Future solution values are inherent in the GFSMMs. However, a purely interpolatory approach is applied for the derivation of the GFSMMs and a detailed theoretical and computational study is presented. These include the order, stability, interval of periodicity, and phase-lag (PL) analysis of the methods. Some of the proposed methods herein possess minimal PL error constants, while some have high-order PL. Also, some of the proposed GFSMMs are P-stable, while some exhibit multiple intervals of periodicity. The application of the newly formulated schemes are demonstrated in the numerical experiments presented.