This paper shows how the geometry of the region affects the conditioning and the accuracy of numerical conformal mapping methods for simply connected regions, especially Fourier series methods. Both explicit examples of popular test cases and more general estimates are discussed. The severe ill conditioning that is known as the crowding phenomenon is discussed and its effect on a conformally transplanted boundary value problem is illustrated. Remarks on various numerical methods are included.
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Thomas K. DeLillo (1994) studied this question.
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