SDE simulation using DifferentialEquations.jl SDE solver RKMilGeneral

Specific Domains Modelling & Simulations
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1

I am simulating an SDE and using scatter! to plot the results.

I set

dt = 0.1 with timespan 0.0 to 1.0,

then if use EM() as the SDE solver method I get 10 equally spaced (in-time) scatter points on the plot.

However, if I use RKMilGeneral for the same purposes I end up with anywhere from 12-19 points plotted, that is 11 to 18 unevenly spaced segments, on the resultant plot.

I am curious as to why this is.

2

With adaptive time stepping, dt is just the initial dt.

https://diffeq.sciml.ai/stable/basics/common_solver_opts/#Basic-Stepsize-Control

  • dt: Sets the initial stepsize. This is also the stepsize for fixed timestep methods. Defaults to an automatic choice if the method is adaptive.
3

Ah okay, under RKMilGeneral it doesn’t say adaptive but I should be familiar enough to know that is the case, is there anyway I can force this to have fixed time-step? I suppose if I need fixed I should be sticking with another method.

4

Any method is adaptive by default. The documentation mentions it the other way around: there’s an explicit mention to any method that is fixed time step only.

  • EM- The Euler-Maruyama method. Strong Order 0.5 in the Ito sense. Has an optional argument split=true for controlling step splitting. When splitting is enabled, the stability with large diffusion eigenvalues is improved. Can handle all forms of noise, including non-diagonal, scalar, and colored noise. Fixed time step only.†

https://diffeq.sciml.ai/stable/basics/common_solver_opts/#Basic-Stepsize-Control

  • adaptive: Turns on adaptive timestepping for appropriate methods. Default is true.

So just use adaptive = false.

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