10. Experimental Design  9. Numerical Methods  9.6.2 The Newton-Raphson method

9.7 Techniques for numerical integration

These techniques will not be covered here, but should be studied elsewhere because they are valuable tools in the analysis of data. Gaussian quadrature is particularly powerful and is used frequently. The Runge-Kutta method and predictor-corrector schemes are among the most important methods for numerical integration of differential equations. These are standard topics in books on numerical methods. For general numerical integration, the author has found the Cash-Karp algorithm described on p. 719 of Press et al. (1992) to be particularly efficient.

SOURCES AND FURTHER READING

Abramowitz, M. and I. A. Stegun, 1972: Handbook of Mathematical Functions. Dover Publications, New York, 1046 pp.

Green, A. W., 1975: An approximation for the shapes of large raindrops. J. Appl. Meteor., 14, 1578-1583.

Hornbeck, R. W., 1975: Numerical Methods. Quantum Publishers, Inc., New York, 310 pp.

Paluch, I. R., 1979: The entrainment mechanism in Colorado cumuli. J. Atmos. Sci., 36, 2467-2478.