stability regions, numerical examples, local error estimation, order conditions, nonstiff initial value problems, explicit Runge-Kutta pairs, explicit general linear methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Stability and convergence of numerical methods for ordinary differential equations, Error bounds for numerical methods for ordinary differential equations