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Hopscotch with nonlinearity
Posted:
Oct 9, 2012 8:20 AM


My understanding of how hopscotch works is that you first compute all the (say) evennumbered points explicitly, and then all the others, also explicitly, but now the calculation is effectively implicit because the second series uses the newly computed values.
We are dealing with a parabolic pde, u_t = u_{xx}
If the pde has a nonlinear term, my feeling is that this too is discretised explicitly in both series of steps, conforming to the hopscotch idea.
I am reading a paper in which the nonlinear term is handled implicitly in the first, "explicit" series, using Newton iteration; this is then followed by the second series, now explicitly. It seems to me that this is not adhering to the hopscotch idea. Some experiments of mine using both methods lead to the same order wrt dT, close to unity, so the Newton thing doesn't help.
Am I right; is the Newton iteration unnecessary or even undesirable (in terms other than cpu time)?
 Dieter Britz



