stepsize control, numerical examples, extended Runge-Kutta-like method, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, absolute stability, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, error estimates, Mesh generation, refinement, and adaptive methods for ordinary differential equations, two-step Runge-Kutta method, Stability and convergence of numerical methods for ordinary differential equations, Error bounds for numerical methods for ordinary differential equations