Is the oscillation in the picture a boundary condition problem?

Hi @Rahul,

As I understand that you are probably thinking that reason for your oscillations are due to arising from insufficient resolution or inappropriate boundary conditions, that is why you keep asking @Torsten to suggest ideas to resolve this issue by asking him “ case I want to keep both I and dI/dx to be not equal to zero,in that case how should I write the bc for right boundary?” and round Robin, so for your boundary conditions, if you want to maintain both the variable ( I ) and its derivative dI/dx non-zero at the right endpoint, you can proceed implementing Robin boundary conditions as follows

% Left and right   boundary conditions

bc = @(xl, ul, xr, ur) deal(ul - 0, qr*ur - pr);

So, in this code snippet, qr and pr are coefficients that you can adjust to control the behavior of the solution at the boundary. I will also suggest that diffusion coefficient sigma is set to a minimum of 1, as values below this can lead to divergence. Additionally, consider using a higher-order method or applying artificial viscosity to dampen oscillations. This approach will help stabilize your solution while maintaining accuracy.

Afterwards, you mentioned “the equation is a convection-diffusion equation, if I wish to use Robin bc, how should I proceed,”, I would proceed by discretizing the domain by defining spatial grid and time steps. Then, setup the equations for interior points by using the standard finite difference approximations for convection and diffusion. Then, at the boundary, replacing the standard boundary conditions with the Robin condition. For example, at the left boundary (i=1):

u(1) = (g - beta * (u(2) - u(1))/dx) / alpha;

Finally, updating your solution iteratively, so that the Robin condition is applied at each time step.