 Romberg's method and Runge–Kutta–Fehlberg are examples of a numerical integration methods which use an adaptive stepsize.For simplicity, the following example uses the simplest integration method, the Euler method; in practice, higher-order methods such as Runge–Kutta methods are preferred due to their superior convergence and stability properties.Consider the initial value problem
where "y" and "f" may denote vectors (in which case this equation represents a system of coupled ODEs in several variables).