Trapezoidal Rule

Definition

a implicit method

$$y_{k+1}=y_k+h\frac{f(t_k,y_k)+f(t_{k+1},y_{k+1})}{2}$$

Stability

It’s sable if

$$|\frac{1+\frac{h\lambda }{2}}{1-\frac{h\lambda }{2}}|\le 1$$

for every $\lambda$ as Eigenvalue