In this paper, we present a method to improve the accuracy of the charge simulation method for numerical conformal mapping. The method constructs the constraint equation by using the charge simulation method. The charges and the conformal radius are computed by using the Runge-Kutta method based on the dynamic system of the constraint equation. By using this method, we can obtain new approximated conformal mapping function and improve the accuracy of numerical conformal mapping compared to the charge simulation method for numerical conformal mapping proposed by Amano. Furthermore, the corresponding numerical results are shown to illustrate the performance of the proposed method.
Conformal mapping is an important issue of complex function theory. In this paper, a new method for numerical conformal mapping of doubly-connected domain is considered. This method calculates the constraint equations of numerical conformal mapping based on charge simulation method of doubly-connected domain using the improvement of iteration method by correcting characteristic values, and the approximate conformal mapping function is constructed using new charge points and conformal mapping radius. We illustrate the efficiency of the proposed method by some numerical results.
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