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Brenton LeMesurier : Conservative Time-Discretization of Stiff Hamiltonian Systems, and Molecular Chain Models

A variety of problems in modeling of large biomolecules and nonlinear optics lead to large, stiff, mildly nonlinear systems of ODEs that have Hamiltonian form. This talk describes a discrete calculus approach to constructing unconditionally stable, time-reversal symmetric discrete gradient conservative schemes for such Hamiltonian systems (akin to the methods developed by Simo, Gonzales, et al), an iterative scheme for the solution of the resulting nonlinear systems which preserves unconditional stability and exact conservation of quadratic first integrals, and methods for increasing the order of accuracy. Some comparisons are made to the more familiar momentum conserving symplectic methods. As an application, some models of pulse propagation along protein and DNA molecules and related numerical observations will be described, with some consequences for the search for continuum limit PDE approximations.

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