boundary conditions for PDE

how do find the correct boundary conditions when with initial condition is: u(x, 0) = atan(x). and the PDE equation is: c*(∂u∂x) + ∂u∂t = 0 ?

Answer 1

[Mohammad Abouali]

This has nothing to do with matlab.

For your linear advection equation, you can use periodic boundary condition, neumann boundary condition or mixture of neumann and Dirichlet.

All of them are valid depending on what you want to do. Just note that the boundary condition should be also valid at time t=0 so consistent with your atan(x) at the boundaries.

Start with Periodic boundary condition, that is the easiest, numerically the most accurate, and usually in most examples people use that anyway.