  We consider the conformal mapping of the Bunimovich stadium, a region
enclosed by a Jordan curve with four smooth corners, primarily in the context
of a particle undergoing Brownian motion within its closed geometry with
Dirichlet boundary conditions. A Chebyshev weighting of the solutions of Symm's
integral equation is employed to give a numerical conformal map of the region
onto the canonical domain of the unit disk in the complex plane. As a measure
of the accuracy of the transformation, the domes' harmonic measure evaluated at
the centre of the stadium is thereby extracted and is compared with results
obtained from Schwarz-Christoffel transformations and Monte Carlo simulations;
the pros and cons of the method are reiterated.
