The authors consider the 2D heat equation \(\partial ( K\partial u/\partial x) /\partial x+\partial ( K\partial u/\partial y) /\partial y+V=\rho c\,\partial u/\partial t\), where \(u\) is the temperature and \(K\) is the non constant thermal conductivity. The problem is posed in a bounded domain of \(\mathbb{R}^{2}\) and various kinds of boundary conditions can be imposed on the boundary: either Dirichlet, or Neumann, or convection, or radiation ones. The authors present the general dual reciprocity method within this context. They write the above equation as \(\nabla ^{2}u=b( x,y,u) \) and, involving the boundary conditions, this dual reciprocity method ends with a system \(\mathbf{Hu-Gq}=\text\textbf{Sb}\), where \(\mathbf{q}\) is the discretization of the flux \(\partial u/\partial n\). The main part of the paper describes the generalized Newmark dual reciprocity method GNpj and the Single Step dual reciprocity method SSpj. The iterations are performed at each time step through a Newton-Raphson method with line searches. The authors then present some computations within this context, considering the different possible boundary conditions. They finally test these methods on an example which is known to present difficulties in the numerical resolution. They consider a square and impose the temperature on two lines of the boundary and the flux on the two other lines. Appropriate values of the data are given. The conclusion of the paper is that GN11 or SS11 can be recommended in order to solve this problem with quite good accuracy.