Algorithm 3.1. $Input:x_1<\cdots <x_n\in [a,b],{\alpha }_1,\dots ,{\alpha }_n\in \mathbb{R}.Output:{\tilde{u}}_1^{+},\dots ,{\tilde{u}}_n^{+}.$

$$\begin{array}{cc}\hfill & 1:j_0=0\text{and}{g}_1=\cdots =g_m=0\hfill \\ \hfill & 2:\hfill \\ \hfill & 3:mainloop:\hfill \\ \hfill & 4:\mathbf{for}j=1,\dots ,n\hfill \\ \hfill & 5:\hfill \\ \hfill & 6:update{g}_1,\dots ,g_{m}and{j}_0:\hfill \\ \hfill & 7:\mathbf{while}{x}_j-x_{j_0+1}>\delta (b-a)\hfill \\ \hfill & 8:\mathbf{for}\mathrm{i}=1,\dots ,\mathrm{m}\hfill \\ \hfill & 9:g_i=g_i{e}^{-(x_{j_0+1}-x_{j_0})t_i}+{\alpha }_i\hfill \\ \hfill & 10:\mathbf{end}\mathbf{for}\hfill \\ \hfill & 11:j_0=j_0+1\hfill \\ \hfill & 12:\mathbf{end}\mathbf{while}\hfill \\ \hfill & 13:\hfill \\ \hfill & 14:computepotentialfrom{x}_{i}suchthat{x}_i\le x_{j_0}:\hfill \\ \hfill & 15:{\tilde{u}}_j^{+}=0\hfill \\ \hfill & 16:\mathbf{for}i=1,\dots ,m\hfill \\ \hfill & 17:{\tilde{u}}_j^{+}={\tilde{u}}_j^{+}-w_i{g}_i{e}^{-(x_j-x_{j_0})t_i}\hfill \\ \hfill & 18:\mathbf{end}\mathbf{for}\hfill \\ \hfill & 19:\hfill \\ \hfill & 20:computepotentialform{x}_{i}suchthat{x}_{j_0+1}\le x_i\le x_{j-1}\hfill \\ \hfill & 21:\mathbf{for}i=j_0+1,\dots ,j-1\hfill \\ \hfill & 22:{\tilde{u}}_j^{+}={\tilde{u}}_j^{+}+{\alpha }_i∕(x_i-x_j).\hfill \\ \hfill & 23:\mathbf{end}\mathbf{for}\hfill \\ \hfill & 24:\mathbf{end}\mathbf{for}\hfill \end{array}$$