Backward Euler method

Implicit, single-stage, first-order, fixed-step, Runge-Kutta method.¹

$$\frac{dy}{dt}=f(t,y)$$ $$t_{n+1}=t_n+h$$ $$k_1=f(t_{n+1},y_{n+1})$$ $$y_{n+1}=y_n+h{k}_1$$

1. Also known as the backward Euler method. ↩