Geodesic
Improving the accuracy of multiple integral evaluation by applying Romberg’s method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 232-240

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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. 
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     title = {Improving the accuracy of multiple integral evaluation by applying {Romberg{\textquoteright}s} method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a2/}
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E. P. Zhidkov; Yu. Yu. Lobanov; V. D. Rushaǐ. Improving the accuracy of multiple integral evaluation by applying Romberg’s method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 232-240. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a2/