Main Idea

1. What?

   Richardson extrapolation applied to results from the Composite Trapezoidal rule can be used for accurate results.

2. Why?

   The technique can be used to obtain high accuracy approximations with little computational cost.

3. Error in Composite Trapezoidal rule:
   

   This implies that Richardsons’ Extrapolation is applicable here.

4. Extrapolation Formula:
   

   Extrapolation then is used to produce \(\mathcal{O}(h_k^{2j})\) approximations by
   

   and according to this table,
   

   Calculate the Romberg table one complete row at a time.

5. Algorithm: