ABSTRACT
In practical applications of conformal mapping of a standard region (the half-plane or the unit disk) onto a problem region which is in the form of a polygon, it becomes necessary to determine approximately the (2n + 2) parameters α 1, …, α n , x 1, …, x n , and the constants C 1 and C 2 that appear in the Schwarz-Christoffel formula (7.1.1). Evaluation of these quantities is known as the parameter problem. We have seen that the mapping functions obtained by using the Schwarz-Christoffel formula involve certain improper integrals which are known as Schwarz-Christoffel integrals. We will discuss methods for numerical solution of these integrals and present Newton’s method for the general case of mapping the upper half-plane onto a quadrilateral.
