A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems

We examine a nonlinear explicit two-step method of fourth algebraic order and infinite phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Applying special vector arithmetic with respect to an analytic function, the method can be extended to be vector-applicable for multidimensional problems. Numerical results to illustrate the efficiency of the method are presented and sensitivity analysis indicates the validity of the method in the frequency regime.