The method can easily be implemented numerically through the following simple algorithm

• Choose the number of mesh points and fix the step.
• calculate \( f(a) \) and \( f(b) \)
• Perform a loop over \( n=1 \) to \( n-1 \) (\( f(a) \) and \( f(b) \) are known) and sum up the terms \( 4f(a+h) +2f(a+2h)+4f(a+3h)+\dots +4f(b-h) \). Each step in the loop corresponds to a given value \( a+nh \). Odd values of \( n \) give \( 4 \) as factor while even values yield \( 2 \) as factor.
• Multiply the final result by \( \frac{h}{3} \).