# Interdisciplinary Applied Mathematics

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coupling. In the following we represent a few schemes that have been used to integrate the DPD equations with various degrees of success. A detailed comparison of the performance of these integrators is given in (Nikunen et al., 2003).

Explicit Euler Forward (EF)

The explicit Euler integrator is never used, but it helps to set the notation for the more complicated algorithms and also as starter for multistep integrators of higher order. We assume that we know the solution at time step n and we want to obtain the solution at time step (n + 1). We update both the velocities and the positions of all particles in a straightforward manner. All three forces contribute within a region refined by the cutoff radius rc.

At time tn+1 we have

,,n+1

v

1

n+1

• At time tn+1 we have

Compute Ff.

Compute physical quantities.

Here the forces at the last step are reevaluated with Vi and гП+1.

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