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……

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Posted by Sriram Ragav on May 24, 2008 at 2:01 am

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Thanks