Composite Rules

Numerical Analysis · Axiom Academy

Dividing intervals for dramatically improved accuracy Instead of one big interval [a, b], divide it into n small subintervals of width h = (b-a)/n. Apply the basic rule to each subinterval, then sum the results. Apply the trapezoid rule to each subinterval. Notice that interior points are shared: Apply Simpson's rule to pairs of subintervals (requires n to be even): How does error decrease as we add more subintervals? Watch how quickly the error decreases as we double n:

This is the written version of the interactive lesson above. See the full Numerical Analysis course.