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ChrisRackauckas avatar ChrisRackauckas commented on June 3, 2024

The commutative integral approximations could be refactored as well

https://github.com/JuliaDiffEq/StochasticDiffEq.jl/blob/master/src/perform_step/low_order.jl#L199-L204

from stochasticdiffeq.jl.

ChrisRackauckas avatar ChrisRackauckas commented on June 3, 2024

#209 adds the approximations, but still a little bit more needs to be done until they are "really" used. The core algorithm to implement here is from https://epubs.siam.org/doi/abs/10.1137/09076636X . SRI1, SRI2, SRS1, and SRS2 should be the most efficient general non-stiff SDE integrators around, so we should implement them (with #209 that should be really easy to do now!).

We also need convergence tests on this. Equation 7.5 from Rossler would serve as a good example. This can be added using the analyticless convergence test helpers from DiffEqDevTools. Example:

https://github.com/JuliaDiffEq/DiffEqDevTools.jl/blob/master/test/analyticless_convergence_tests.jl#L20-L34

from stochasticdiffeq.jl.

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