Dirichlet boundary conditions

It is otherwise called the periodic boundry conditions.

The idea behind periodic BCs is that whatever goes out comes in. For a domain [-1,1] periodic B.C. simply means that you set u(1,t) = u(0,t) for all t. This means that u(1,t) which comes from the update formula (in your case, say Lax-Fredrich scheme) must be assigned to u(0,t) which cannot be updated otherwise (You can see that every point execpt the leftmost is updated using the Lax-Fredrich formula or for that matter any first or second order explicit schemes). Of course to start with, we have the initial conditions from the general solution given by u(1,0)=u(-1,0)=0. Also, note that LF method is the most dissipative of all schemes (it is only first order) and therefore the dissipation will reflect as a loss in amplitude. And you have many higher order methods to deal with other problems……


1 Comment »

  1. 1
    Your Girlfriend Says:


RSS Feed for this entry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: