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The accumulation of this small error over long time steps may cause problems or instabilities in the simulation.
The slow motions would then be modeled with a three-dimensional system that is solved explicitly with long time steps that are determined by the slow wave speeds.
The scheme conserves mass, overcoming problems of mass conservation typically experienced with offline transport models, and permits long time steps (relative to the Courant number) to be used by the offline model.
A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps.
Because the physical size, shape, and regulatory state of a colony changes relatively slowly, fairly long time steps, tgrow, can be safely taken between updates.
Depending on the dynamics of the system, long time steps may cause three problems: (1) the window is large and the size of the matrix Q j may exceed the working memory capacity, (2) the dynamics of the system may differ considerably during a long time step and Q j has bad mathematical properties, (3) the window may contain states that are only significant during a much shorter time interval.
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We can then use the results of the "short" steps to find the quantities needed to calculate the change in the full distribution f(Z, Vz, Vp) during a single "long" time step.
The method used here has the effect of introducing a type of time filtering into the forcing for the layer equations, which are solved with a long time step.
A commonly used alternative is to confine the fast waves to a two-dimensional system, via vertical averaging, and then to compute the remaining motions explicitly with a long time step.
We intentionally used the rather long time step (1 s) in order to acquire fluorescence recovery over the optimal time range (90 s) for investigation of L-plastin binding and actin polymerization properties.
In the case of time-dependent FBA, choosing the time step intervals for the simulation implies a trade-off between the risk of propagating an error due to the numerical solution in case of a long time step and the high computation time in case of a short time step.
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