Conformal mapping of circular arc polygons. The authors describe an algorithm which computes the conformal mapping from the unit disk onto a simply connected region bounded by circular arc sides (straight sides are regarded as special cases of circular arc sides). This conformal mapping problem is a generalization of the problem which Trefethen solved by his Schwarz-Christoffel program [straight sides only, see L. N. Trefethen, SIAM J. Sci. Stat. Comput. 1, 82-102 (1980; Zbl 0451.30004)]. Instead of using Gauss-Jacobi quadrature to evaluate the Schwarz-Christoffel integral, the authors applied an ordinary differential equation solver to a non-singular formulation of the Schwarzian differential equation. The unknown parameters of this differential equation are determined by solving a nonlinear least square problem. The authors coded the algorithm as a FORTRAN program; computational results are given. (netlib conformal)