Journal of the
Korean Mathematical Society JKMS

We employ a hyperbolic tangent function to construct non-linear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

Keywords: hyperbolic tangent, weakly singular integral, Cauchy principal value integral, non-linear transformation

MSC numbers: 65D30, 65D32, 41A55