Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs

We elaborate on a nonlinear explicit two-step P-stable method of fourth algebraic order and varying phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Using 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.