Algorithm 1 Picard method.

1:Choose a small positive value ${\epsilon }_{non}$ and take ${\mathbf{U}}^{n+1,0}={\mathbf{U}}^n\ge 0$. 2:for$k=1,2,...$do 3:     Solve the linear system $$\begin{array}{c}\hfill \begin{array}{c}\hfill \mathbb{M}\left({\mathbf{U}}^{n+1,k}\right){\mathbf{U}}^{n+1,k+1}=\mathbf{F}\left({\mathbf{U}}^n\right)\end{array}\end{array}$$ (25) to obtain ${\mathbf{U}}^{n+1,k+1}$. 4:     Use $$\begin{array}{c}\hfill \begin{array}{c}\hfill \parallel \mathbb{M}\left({\mathbf{U}}^{n+1,k+1}\right){\mathbf{U}}^{n+1,k+1}-\mathbf{F}\left({\mathbf{U}}^{n+1,k+1}\right)\parallel \le {\epsilon }_{non}\parallel \mathbb{M}\left({\mathbf{U}}^n\right){\mathbf{U}}^n-\mathbf{F}\left({\mathbf{U}}^n\right)\parallel \end{array}\end{array}$$ (26) as the convergence criterion. 5:end for