A fully numerical method based on double exponential formulas for strongly singular volume integrals

In this study we utilize quadrature rules based on double exponential formulas to evaluate strongly singular volume integrals. First it is shown numerically that double exponential formulas generate efficient quadrature rules for weakly singular volume integrals. Then, the strongly singular volume integrals are calculated by evaluating the second derivative of the weakly singular integral numerically. By using some test integrals it is shown that accurate results can be obtained by the proposed procedure.