SDE Solvers

SDE Solvers

Recommended Methods

For most diagonal and scalar noise problems where a good amount of accuracy is required and stiffness may be an issue, the SRIW1Optimized algorithm should do well. If the problem has additive noise, then SRA1Optimized will be the optimal algorithm. For non-commutative noise, EM and EulerHeun will be the most accurate (for Ito and Stratonovich interpretations respectively).

Special Keyword Arguments

Full List of Methods

StochasticDiffEq.jl

Each of the StochasticDiffEq.jl solvers come with a linear interpolation.

Example usage:

sol = solve(prob,SRIW1())

For SRA and SRI, the following option is allowed:

†: Does not step to the interval endpoint. This can cause issues with discontinuity detection, and discrete variables need to be updated appropriately.

StochasticCompositeAlgorithm

One unique feature of StochasticDiffEq.jl is the StochasticCompositeAlgorithm, which allows you to, with very minimal overhead, design a multimethod which switches between chosen algorithms as needed. The syntax is StochasticCompositeAlgorithm(algtup,choice_function) where algtup is a tuple of StochasticDiffEq.jl algorithms, and choice_function is a function which declares which method to use in the following step. For example, we can design a multimethod which uses EM() but switches to RKMil() whenever dt is too small:

choice_function(integrator) = (Int(integrator.dt<0.001) + 1)
alg_switch = StochasticCompositeAlgorithm((EM(),RKMil()),choice_function)

The choice_function takes in an integrator and thus all of the features available in the Integrator Interface can be used in the choice function.