Optimization of two-step method with Bhaskara points for solving non-linear dynamical problems

We derive a two-step method for solving non-linear dynamical problems employing Bhaskara points as off grid points. Deterministic in nature, non-linear dynamical systems display a periodic behavior that is highly dependent on the beginning circumstances, making long-term predictions impossible. Four Bhaskara points are generated as hybrid points to optimized the system. The method is use to solve nonlinear dynamical systems to demonstrate the accuracy and efficient of the method. The method is zero stable and consistent. Some examples from literature were considered to demonstrate the efficiency and the accuracy of the method.