Implicit midpoint rule
= Implicit midpoint rule
= Implicit midpoint method
{synonym}
The implicit midpoint rule advances an autonomous ordinary differential equation by
$$
y_{n+1}=y_n+h f\left(\frac{y_n+y_{n+1}}2\right).
$$
It is a second-order, <A-stable>, <time-symmetric numerical method>.
The <implicit midpoint rule> is the <midpoint method> with $y_{n+1}=y_n+h f(t_n+h/2,(y_n+y_{n+1})/2)$. It is a one-stage <implicit Runge-Kutta method>.