One-step method (source code)

= One-step method
{title2=$y_{n+1}=y_n+h\Phi(x_n,y_n,h)$}

A one-step method approximates an <ordinary differential equation> using the current approximate solution and evaluations within the next step. The function $\Phi$ is its increment function. A <Runge-Kutta method> may use several intermediate stages while remaining a one-step method: it does not require additional previous solution values as a <linear multistep method> does. Its <consistency error> is the exact-start update defect divided by $h$.