 | Java Number Cruncher: The Java Programmer's Guide to Numerical Computing
By Ronald Mak
| | Table of Contents | | | | Chapter 7. Numerical Integration |
References Chapra, Seven C., and Raymond P. Canale, Numerical Methods for Engineers , 3rd edition, New York: WCB/McGraw-Hill, 1998. Cheny, Ward, and David Kincaid, Numerical Mathematics and Computing , 4th edition, Pacific Grove, CA: Brooks/Cole, 1999. Woodford, C., and C. Phillips, Numerical Methods with Worked Examples , London: Chapman and Hall, 1997.
Sections 21.1 and 21.2 of Chapra and Chapter 4 of Woodford provide excellent introductions to the trapezoidal and Simpson's integration algorithms. Chapra also has good coverage of other integration algorithms in the rest of Chapter 21 and in Chapter 22. Cheney, in Section 5.4, presents an adaptive Simpson's algorithm, which dynamically determines whether or not to subdivide intervals based on the nature of the integrand. Hamming, Richard W., Methods of Mathematics Applied to Calculus, Probability, and Statistics , Englewood Cliffs, NJ: Prentice-Hall, 1985.
This book contains a very clear derivation of Simpson's formula for parabolas in Section 11.11.  |
