Physics 22 Reading List #4

A few hints for the relaxation method in the current homework set:

• Because we have the special case of Dirichlet boundary conditions (and only in this special case), it suffices to iterate over only the non-boundary points in the relaxation algorithms, as long as you have first set the boundary points appropriately.
• Except for the SOR method, you may need to take many (i.e. hundreds or possibly thousands of) iterations to achieve convergence to some desired accuracy. SOR converges much more quickly.
  
• You should think about the difference between two different types of error that appear:
  
  1. Error associated with not having run the relaxation to t -> infinity.
  2. Error associated with the finite-difference representation of the spatial derivatives.
     
  
  These two error sources are largely independent, and in your results you should be able to determine the size of each.