End-correction integration formulae with optimized terminal sampling points
✍ Scribed by Paolo Luchini
- Book ID
- 103048852
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 767 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0010-4655
No coin nor oath required. For personal study only.
✦ Synopsis
A new family of integration rules is presented that optimizes the choice of terminal sampling points in a Gregory-type end-correction formula. Besides applying the various methods to a number of test functions as is traditionally done, a comparison between the new and the classical numerical integration rules is conducted by the Fourier method, which allows their approximation properties to be estimated not only in the limit of step size tending to zero but also for nonzero step size. From these tests our optimized rule turns out to surpass all the other methods, including past improvements of the Gregory rule such as the Gauss-Gregory and Hamming-Pinkham rules.