Romberg Integration

A powerful Numerical Integration technique which uses $k$ refinements of the extended Trapezoidal Rule to remove error terms less than order ${\mathcal O}(N^{-2k})$. The routine advocated by Press et al. (1992) makes use of Neville's Algorithm.

References

Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., pp. 106-107, 1990.

Dahlquist, G. and Bjorck, A. §7.4.1-7.4.2 in Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall, 1974.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Romberg Integration.'' §4.3 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 134-135, 1992.

Ralston, A. and Rabinowitz, P. §4.10 in A First Course in Numerical Analysis, 2nd ed. New York: McGraw-Hill, 1978.

Stoer, J.; and Bulirsch, R. §3.4-3.5 in Introduction to Numerical Analysis. New York: Springer-Verlag, 1980.