On the numerical evaluation of a particular singular two-dimensional integral
Authors: G. Monegato and J. N. Lyness
Journal: Math. Comp. 33 (1979), 993-1002
MSC: Primary 65D30; Secondary 65B05
MathSciNet review: 528052
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Abstract: We investigate the possibility of using two-dimensional Romberg integration to approximate integrals, over the square , , of integrand functions of the form where 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 has a point singularity of a specified nature at the origin.
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