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)+⋯+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 h3.