Numerical solutions to a class of two dimensional harmonic mixed boundary value problems defined on rectangular domains and containing singularities are obtained using conformal transformation methods. These map the original problems into similar ones containing no singularities, and to which analytic solutions are known. Although the mapping technique produces analytic solutions to the original problems, these involve elliptic functions and integrals which have to be evaluated numerically, so that in practice only approximations can be obtained. Results calculated in this manner for model problems compare favourably with those obtained previously by other methods. On this evidence, and because of the ease with which the method can be adapted to different individual problems, we strongly recommend the transformation technique for solving problems of this class.
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