A two-step explicit P-stable method of high phase-lag order for linear periodic IVPs

In this paper, we present a nonlinear two-step explicit P-stable method of fourth algebraic order and 12th phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Based on a special vector arithmetic with respect to an analytic function, the method can be extended to be vector-applicable for multi-dimensional problems directly. Some numerical results are reported to illustrate the efficiency of the method.