On the numerical evaluation of a particular singular two-dimensional integral
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- by G. Monegato and J. N. Lyness PDF
- Math. Comp. 33 (1979), 993-1002 Request permission
Abstract:
We investigate the possibility of using two-dimensional Romberg integration to approximate integrals, over the square $0 \leqslant x$, $y \leqslant 1$, of integrand functions of the form $g(x,y)/(x - y)$ where $g(x,y)$ is, for example, analytic in x and y. We show that Romberg integration may be properly justified so long as it is based on a diagonally symmetric rule and function values on the singular diagonal, if required, are defined in a particular way. We also investigate the consequences of ignoring fhese function values (i.e. setting them to zero) in the context of such a calculation. We also derive the asymptotic expansion on which extrapolation methods can be based when $g(x,y)$ has a point singularity of a specified nature at the origin.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 993-1002
- MSC: Primary 65D30; Secondary 65B05
- DOI: https://doi.org/10.1090/S0025-5718-1979-0528052-6
- MathSciNet review: 528052