numerical examples, Runge-Kutta methods, stiff systems, method of exponential time differencing, Nonlinear ordinary differential equations and systems, stability, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, linearly implicit methods, spectral methods, Initial value problems for higher-order parabolic equations, Stability and convergence of numerical methods for ordinary differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs