I need to come up with a boundary condition function for a PDE solving method desribed here: https://github.com/sciann/sciann-applications/blob/master/SciANN-BurgersEquation/SciANN-BurgersEquation.ipynb
The condition is $$u(x=-1,t)=u(x=1,t)$$ The way I see it I need to come up with two expression:
- Expression 1: $g_1(x) * u$ st. $g =0$ when $x\neq -1$ and $g=1$ for $x=-1$
- Expression 2: $g_2(x) * u$ st. $g =0$ when $x\neq1$ and $g=1$ for $x=1$
Then my BC condition function $f$ is $$f=g_1u-g_2u$$ which in solving process is set to $f=0$. How should I formulate this function? I probably need some sigmund function but, right? Please help