Volume 14, Number 3, Fall 2006
STRUCTUREPRESERVING AND
EXPONENTIAL DISCRETIZATIONS
OF INITIAL VALUE PROBLEMS
JOHN C. BOWMAN
Abstract. Specialized integration algorithms for initial
value problems, obtained by applying conventional explicit discretizations
in a transformed space, are described. One example,
conservative integration, is motivated by a theorem of Ge
Zhong and Marsden [17] that establishes that in the absence of
explicit time dependence, one must in practice choose between
preserving symplecticity or conserving the Hamiltonian. Another
example, exponential integration, is well suited to highly
stiff ordinary differential equations. Fully Lagrangian methods
for advection are shown to be a special case of exponential
integration.
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