Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MULTISCALE DISCRETIZATION OF
ELECTRIC-FIELD EQUATIONS
By
Shu-Jen Huang
May 2005
Chair: William W. Hager
Major Department: Mathematics
We develop stable finite-difference approximations for equations describing the
electric field between the surface of the Earth and the ionosphere. In this scheme,
we introduce a parameter p in the time discretization. For example, 1 = 0 and
pI = 1 give us forward and backward difference methods respectively, and p = 1/2 is
the Crank-Nicholson scheme. The approximations are unconditionally stable when
1/2 < p < 1 and unstable when 0 < p < 1/2. Max-norm error estimates for the
discrete approximations are established. We show that the error is O(At)2 + 0(h2)
if p = 1/2, and O(At) + 0(h2) otherwise. We conduct numerical experiments to
verify our analysis.