Search results
Results from the WOW.Com Content Network
For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system.
Alternatively, a few explicit solvent molecules can be added to a QM region and the rest of the solvent treated implicitly. Previous work has shown mixed results upon the addition of explicit solvent molecules to an implicit solvent. One example added up to three explicit water molecules to a QM calculation with an implicit COSMO water model.
Implicit solvation (sometimes termed continuum solvation) is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of molecular mechanics.
Static vs. dynamic. A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations or difference equations. Explicit vs. implicit.
The term, "molecular model" refer to systems that contain one or more explicit atoms (although solvent atoms may be represented implicitly) and where nuclear structure is neglected. The electronic structure is often also omitted unless it is necessary in illustrating the function of the molecule being modeled.
The Crank–Nicolson stencil for a 1D problem. The Crank–Nicolson method is based on the trapezoidal rule, giving second-order convergence in time.For linear equations, the trapezoidal rule is equivalent to the implicit midpoint method [citation needed] —the simplest example of a Gauss–Legendre implicit Runge–Kutta method—which also has the property of being a geometric integrator.
Understanding Nonlinear Dynamics. New York: Springer. ISBN 978-0-387-94440-1. Leigh, E. R. (1968). "The ecological role of Volterra's equations". Some Mathematical Problems in Biology. – a modern discussion using Hudson's Bay Company data on lynx and hares in Canada from 1847 to 1903. Murray, J. D. (2003). Mathematical Biology I: An ...