I want a int of how to set the resolution (using Newton Raphson method) in order to solve this equation :
$$ k_1 = f(t_i+ \frac{1}{2} h, y_1 + \frac{1}{2}k1) $$
I'm using python but I want understand the step
This formula is used in order to compute the 2nd order IMPLICIT Runge kutta methods, suitable for solving stiff system of differential equations. after compute $k1$ the solution of equations is $$ y_{i+1} = y_i + k1 h$$
EDIT It is an implicit Runge Kutta method!!