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Merge pull request #88 from darwindarak/patch-1
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Fix some typos in `PCEuler` docs
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ChrisRackauckas committed Jun 18, 2018
2 parents 505fd58 + 26f85d7 commit d3a13be
Showing 1 changed file with 17 additions and 11 deletions.
28 changes: 17 additions & 11 deletions src/algorithms.jl
Original file line number Diff line number Diff line change
Expand Up @@ -39,18 +39,24 @@ struct PCEuler{T<:Real, F} <: StochasticDiffEqAlgorithm
ggprime::F
end


"""
Predictor Corrector Euler -
args: ggprime::Function
For scalar problems, ggprime = b*\partial_x(b)
For multi-dimensional problems
bbprime_k = sum_{j=1...M, i=1...D} b^(j)_i \paritial_i b^(j)_k
where b^(j) correspond to the noise vector due to the j'th noise channel.
If problem is in place - a in place ggprime should be supplied - and vice versa for not in place speicification of problem.
kwargs: theta::Real
Degree of implicitness in the drift term. Set to 0.5 by default.
eta::Real
Degree of implicitness in the diffusion term. Set to 0.5 by default.
PCEuler(ggprime; theta=1/2, eta=1/2)
Predictor Corrector Euler
# Arguments
- `ggprime::Function`:
For scalar problems, `ggprime` ``= b\\partial_x(b)``
For multi-dimensional problems
`bbprime_k` ``= \\sum_{j=1...M, i=1...D} b^(j)_i \\partial_i b^(j)_k``
where ``b^(j)`` correspond to the noise vector due to the j'th noise channel.
If problem is in place - a in place ggprime should be supplied - and
vice versa for not in place speicification of problem.
- `theta::Real`:
Degree of implicitness in the drift term. Set to 0.5 by default.
- `eta::Real`:
Degree of implicitness in the diffusion term. Set to 0.5 by default.
Reference: Stochastics and Dynamics, Vol. 8, No. 3 (2008) 561–581
Note that the original paper has a typo in the definition of ggprime...
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