  Many authors have studied the numerical computation of conformal mappings
(numerical conformal mapping), and there are nowadays several efficient
numerical schemes. Among them, Amano's method offers a straightforward
numerical procedure for computing conformal mappings based on the method of
fundamental solutions, and it has been applied to several regions with great
success. However, there are some difficulties in constructing a suitable
conjugate harmonic function; therefore, it is required a little of
craftmanship. In this paper, we construct another numerical scheme for
computing conformal mappings based on the dipole simulation method and give
mathematical theorems on the approximation error and the arrangements of the
singular points. Several numerical results are also presented in order to
ensure the effectiveness of our proposed method.
