# What is romberg's and monte carlo method?

1. Jun 9, 2005

### isabella

anybody knows what is romberg's method and monte carlo method?

2. Jun 10, 2005

### steven187

hello isabella

Romberg integration is an application of Richardson’s extrapolation, using the Trapezoidal Rule as the fundamental method of approximation.

One may present Romberg’s integration process in a lattice form, where the values in the first column are computed using the Composite Trapezoidal Rule and the remainder using Richardson’s extrapolation: that is by the formulae

$$T_{2n}^{(k)} =\frac{4^kT_{2n}^{(k-1)}-T_{n}^{(k-1)}}{4^k-1}$$

then the last value in the lattice will give you an approximation to the area under the curve

and for the monte carlo iv already explained it in your other post if you have have any problems, elaborate on what you have problems understanding

steven