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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 2, Pages 232–240 (Mi zvmmf35)  
This article is cited in 2 scientific papers (total in 2 papers)

Improving the accuracy of multiple integral evaluation by applying Romberg’s method

E. P. Zhidkov, Yu. Yu. Lobanov, V. D. Rushaĭ

Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia
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Abstract: Romberg’s method, which is used to improve the accuracy of one-dimensional integral evaluation, is extended to multiple integrals if they are evaluated using the product of composite quadrature formulas. Under certain conditions, the coefficients of the Romberg formula are independent of the integral’s multiplicity, which makes it possible to use a simple evaluation algorithm developed for one-dimensional integrals. As examples, integrals of multiplicity two to six are evaluated by Romberg’s method and the results are compared with other methods.
Key words: numerical integration, multiple integrals, Romberg’s method.
Received: 24.05.2007
Revised: 03.03.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 2, Pages 224–231
DOI: https://doi.org/10.1134/S0965542509020031
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
Language: Russian
Citation: E. P. Zhidkov, Yu. Yu. Lobanov, V. D. Rushaǐ, “Improving the accuracy of multiple integral evaluation by applying Romberg’s method”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 232–240; Comput. Math. Math. Phys., 49:2 (2009), 224–231
Citation in format AMSBIB
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