The Mullins–Sekerka problem is numerically solved in \({\mathbb {R}}^2\) with the aid of the charge simulation method. This is an expansion of the numerical scheme by which Sakakibara and Yazaki computed the Hele–Shaw flow. We investigate a relationship among a time step, the number of collocation points and the position of singular points to ensure that the length of the generated approximate polygonal curves gradually decreases. We propose a new benchmark function for the Mullins–Sekerka flow to confirm that the scheme works well. Moreover, by changing the fundamental solutions of the charge simulation method, we are successful to establish a numerical scheme that can be used to treat the Mullins–Sekerka problem with the contact angle condition.
