Solution of the two-dimensional heat equation for a square in terms of elliptic functions

In this study, an alternative method is presented for the solution of two-dimensional heat equation in a square region. In this method, the solution function of the problem is based on the Green function, and therefore on elliptic functions. The numerical results have been computed for an application example and compared with the results of the well-known method of separation of variables and the finite elements method. The comparison study shows that the present method gives better results than those of the other methods.