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Topic: Hopscotch with nonlinearity
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Dieter Britz

Posts: 20
Registered: 6/17/10
Hopscotch with nonlinearity
Posted: Oct 9, 2012 8:20 AM
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My understanding of how hopscotch works is that you
first compute all the (say) even-numbered 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

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