Odd Order Integrator with Two Complex Functions Control Parameters for Solving Systems of Initial Value Problems

In this study, a numerical integrator that is based on a nonlinear interpolant, for the local representation of the theoretical solution is presented. The resulting integrator aims to solve second and higher-order initial value problems as systems of first-order initial value problems. The method is designed to have two complex functions as control parameters. The control parameters may become real, depending on the nature of the second-order initial value problems to be solved. The generalization and properties of the scheme are also presented.