Abstract

Chapter 2
Temporal Integration
2.1 Integrator Selection
To advance in time, we give the system of ODEs coming from the discretization to
a numerical integrator. Since we want to reduce computation time, the choice of
integrator is important. We tested the problem with two integrators: ROCK4 and
VODEPK. In Figure 2.1, a flow chart is given to show how the nonlinearity in the
problem is handled (that is, how the potential U is computed from f).
Integrators are computer software that numerically solve an ODE. The typically
problem they solve come in the form dy
dt
= G(y, t) with given initial condition y(0) = y0
where y ∈ R M . These integrators are given a time t ∗ , the initial condition y 0 ∈ R M ,
Current f-value Compute n(x)
Poisson solve Add band-offset
for u(x)
Figure 2.1: Flow Chart for Computing U
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New U(x)