  We study numerical computation of several conformal invariants of simply
connected domains in the complex plane including, the hyperbolic distance, the
reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The
method we use is based on the boundary integral equation with the generalized
Neumann kernel. Several numerical examples are presented. We validate the
performance and accuracy of our method by considering several model problems
with known analytic solutions.
