Trapezes integration method

The integral form of the ordinary first-order differential equation is written:

\[\int_{t_{i}}^{t_{i+1}}\frac{dy}{dt} = \int_{t_{i}}^{t_{i+1}}f(y,t)\]

Trapezes methods gives:

\[y_{i+1} \simeq y_i + \frac{y'_i + y'_{i+1}}{2} \Delta t\]