Consider evaluating the following numerical integral
Both Maple and Mathematica could not give an answer due the singularities lie along x=y. What we will do is to transform the singularities to the boundary first and apply a quadrature which uses uniformly regular matrices for computations.
Note that the function is symmetric with respect to y=x, so we consider the integration over the triangle with vertices O=(0,0), P=(1,0) and Q=(1,1). After the transformation with change of variables, u=x, and v=x-y, the singular points are shifted to x- axis, and the Jacobian is Thus, equation (1) becomes By using the uniformly regular matrices and and write a corresponding Pascal program, we obtain the following information