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Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme.
The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is accounted for.
On the other hand, the immersed boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization.
The numerical method for the fluid mechanical model integrates the compressible Navier Stokes equations using an explicit time advancement scheme and high-order finite differences.
However, all methods face a very restrictive time step when using an explicit time advancement scheme in the azimuthal direction, where cell sizes are of the order O Δr rΔθ)).
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The equation is then solved incrementally through the whole time history using an explicit time-marching approach.
Details of the choice of parameter values are given in additional file 2. Most previous models have used an explicit time delay to model transcription and translation (for example, see [ 16- 18]).
Here, an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method.
In one-, two-, and three-dimensional simulations, the cable equation: (2) ∂ t V = ∇ · D ∇ V − I i o n + I s t i m was integrated in time using an explicit Euler scheme with a time step of Δ t = 0.02 ms and a spatial resolution of Δ x = 150 μm.
The filtered Navier Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid.
Equation [ 2] is a typical reaction-diffusion equation that is solved independently for nutrients and signals on a rectangular grid with periodic boundary conditions using an explicit finite difference method, at each time point of the simulation.
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