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On a Modification of Romberg Quadrature

Published online by Cambridge University Press:  20 November 2018

R. Manohar  and
C. Turnbull
C. Turnbull
Affiliation:
University of Saskatchewan, Saskatoon, CAO Department of Transport, Montreal International Airport, Dorval, Que.
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Meir and Sharma [1] have suggested a modification of Romberg quadrature using Newton-Cotes and, in particular, Simpson sums in place of trapezoidal sums. By comparing the error term with that obtained by Bulirsch [3] for trapezoidal sums, they concluded that the use of Simpson sums would lead to an improvement of the results. The procedure adopted by Meir and Sharma [1] permits them to obtain an expression for the error in the numerical quadrature. However, for the purpose of numerical computation, this procedure appears to be less suitable. In section 3, we give an alternative formulation which would enable us to carry out the computation, using Simpson sums, in the same wasy as is done in the case of Romberg quadrature with trapezoidal sums. Some numerical results are discussed in section 4.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 217 - 224
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Meir, A. and Sharma, A., On the method of Romberg quadrature. J. SIAM Numer. Anal.(Ser. B) 2 (1965) 250-258.Google Scholar
2. Bauer, F.L., Rutishauser, H. and Stiefel, E., New aspects in numerical quadrature. Proc. symp. in Appl. Math. 15 (Amer. Math. Soc., 1963)199-218.Google Scholar
3. Bulirsch, R., Bemerkungen zur Romberg-Integration. Num. Math. 6 (1964) 6-16. 223Google Scholar
4. Turnbull, C., A study of some methods of numerical quadrature. Master's Thesis (Univ. of Saskatchewan, Saskatoon, 1967).Google Scholar