Add boost::odeint's Cash-Karp integrator

[yizhang-yiz]

Description

This issue is spawned out of the benchmark in #2326 , where additional integrators from odeint & arkode was evaluated. In particular, boost::odeint's Cash-Karp method(ckrk) that has better stability shows to be an potential addition to our integrators.

Example

WIP branch: cash_karp_ckrk.

• further benchmark based on runing 4-chain sampling using 10 random seeds in each model.

  lokta-volterror

  In this model ckrk has 4 chains "stuck", indicated by much greater # of leapfrogs. Plots below excludes those chains.

  SIR

  

  mildly-stiff Van del Pol oscillator

  

• describe the expected behavior if the feature exists Same as rk45: ode_ckrk(...) with implementation based on boost::odeint.

Expected Output

Same integrator output but potentially more efficient when parameter sampled causes the system to be stability-constrained.

Current Version:

v3.4.0

@bbbales2 @wds15

[bbbales2]

That seems better. What is different between the two? Is this a choice that someone could make or is it always guess and check?

[yizhang-yiz]

@bbbales2 ckrk has a greater stability region than rk45 so it's more stable, and it's designed for problems with large derivatives and/or rapid oscillations. So it suits better for ODEs that could be sampled into mild stiffness(the SIR & Van del Pol example above). For non-stiff problem it could cause slow down by trying too hard on parameters that could be right-out rejected(the Lotka-Volterra example).