Setting up the network is done in similar matter as for the example of solving the diffusion equation. The only things we have to change, is the trial solution such that it satisfies the conditions from (20) and the cost function.
The trial solution becomes slightly different since we have other conditions than in the example of solving the diffusion equation. Here, a possible trial solution \( g_t(x,t) \) is
$$ g_t(x,t) = h_1(x,t) + x(1-x)t^2N(x,t,P) $$
where
$$ h_1(x,t) = (1-t^2)u(x) + tv(x) $$
Note that this trial solution satisfies the conditions only if \( u(0) = v(0) = u(1) = v(1) = 0 \), which is the case in this example.