Boundary and Initial condition for PDE

Boundary and Initial condition are way to imporatant as PDE have infinite solution and to find the unique or desired solution for our PDE equation we need to define its boundary and initial conditions.

We need to define a domain for a specific 1d or 2d aspect , like for nozzle or diffuser. In that domain we define that how our boundary and initial condition are taken by us. The boundary condition is a set of constraints that define the behavior of unknown functions on the spatial boundary of the domain.

Sometime a boundary condition cannot define the exact solution and in that case we need to desine the initial condition in which we tell that at what initial velocity or time we are considiring the case.

These conditions gets changed with type of PDE in equation as for each type of equations have different conditions and each type of equations have different methods to solve them mainly EXPLICIT and IMPLICT method. Hence these conditions get changed.