Efficient 2nd Order Taylor Series Expansion Model to Integrate Stiff and Non-Linear ODEs: Comparison to Rk45-Type Integrators

A Taylor Series Expansion (TaSE) and three Runge-Kutta RK45 embedded pairs numerical integrators of ordinary differential equations (ODEs) are developed. The TaSE model is designed to solve higher order (>1) ODEs. Validation of TaSE was carried out by help of the RK45 models as well as exact solution for well-chosen stiff test cases. The model implementation and its local and global order of accuracy are investigated.