Romberg Nested Extrapolation

Romberg integration combines the composite trapezoidal rule with Richardson extrapolation. It systematically evaluates the trapezoidal rule at a series of refined step sizes, then eliminates the error terms algebraically.

Experiment

You can reproduce this behavior in the interactive module.

1. Set the Function to Quartic.
2. Set the Refinement level to 2.
3. Set the Column to 2.
4. Observe that the Romberg value is exactly 0.2, while the raw trapezoid value is 0.220703125.
5. Change the Function to Sine and note how increasing the column progressively improves the Romberg value towards the exact integral.