A comparison of the error function and the tanh transformation as progressive rules for double and triple singular integrals

摘要

Transformations of the form x = tanh(g(t)) for g(t) = n and for g(t) = c sinh(t), as well as transformations of the error function type are employed on double and triple singular integrals. Extensions of the one-dimensional approach allow variable limit multiple integrals to be attempted successfully. Some shortcomings of the double exponential or DE rule are exposed in the comparisons. Finally, comparison is made with the method of good lattice points (Sugihara, 1987).