Romberg’s method

Romberg s Method Rombergs method uses extrapolation techniques to improve the answer (Ref. 231). If we let Zi be the value of the integral obtained using intei val size h = Ax, and I9 be the value of I obtained when using interval size h/2, and Zq the true value of I, then the error in a methoa is approximately/ ", or... 

Romberg s method is most useful for a low-order method (small m) because significant improvement is then possible. 

This gives a good estimate provided At is small enough that the method is truly convergent with order p. This process can also be repeated in the same way Romberg s method was used for quadrature. 

As an example of the application of Romberg s method, consider the integral... 

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