Please consider the assignment I have uploaded on the picture.
I am confused about the functions $g_L(t)$, $g_R(t)$ and $\eta(x)$. What are they and how do I find them... My question:
Is it possbile to find out how $g_L(t)$, $g_R(t)$ and $\eta(x)$ look like purely based on this formulation?
In order to solve this problem I need to know what the functions look like but unfortunately I don't how to determine the functions.
(EDIT: If those are not given; How can I find suitable function so I can make an numeric implementation?)
I am using the book Finite Difference Methods for Ordinary and Partial Differential equations by LeVeque. In chapter 9 it is presented how to solve the Heat equation but all the methods are based on knowing $g_L(t)$, $g_R(t)$ and $\eta(x)$ beforehand, which means I have overlooked some simple theory about Dirichlet boundary conditions?.