We assume now that we have an estimate for the unknown functions u11, u_{12} , u_{21} and u_{22} . We will call this the zeroth value and label it as u^{(0)}_{11} , u^{(0)}_{12} , u^{(0)}_{21} and u^{(0)}_{22} . We can then set up an iterative scheme where the next solution is defined in terms of the previous one as \begin{align} u^{(1)}_{11} =&\frac{1}{4}(b_1-u^{(0)}_{12} -u^{(0)}_{21}) \nonumber \\ u^{(1)}_{12} =&\frac{1}{4}(b_2-u^{(0)}_{11}-u^{(0)}_{22}) \nonumber \\ u^{(1)}_{21} =&\frac{1}{4}(b_3-u^{(0)}_{11}-u^{(0)}_{22}) \nonumber \\ u^{(1)}_{22}=&\frac{1}{4}(b_4-u^{(0)}_{12}-u^{(0)}_{21}), \nonumber \end{align} where we have defined the vector \begin{equation*} \mathbf{b}= \begin{bmatrix} u_{01}+u_{10}-\tilde{\rho}_{11}\\ u_{13}+u_{02}-\tilde{\rho}_{12}\\ u_{31}+u_{20}-\tilde{\rho}_{21} \\ u_{32}+u_{23}-\tilde{\rho}_{22}\\ \end{bmatrix}. \end{equation*}