Table 1 An overview of the Hy3S numerical methods
From: Multiscale Hy3S: Hybrid stochastic simulation for supercomputers
Name | Advantages | Disadvantages |
|---|---|---|
Next Reaction variant of SSA | Essentially exact | Extremely slow for 'large' systems |
HyJCMSS Fixed Euler-Maruyama | HyJCMSS methods are much faster for 'large' systems. Fastest SDE numerical integrator for non-stiff systems. | For stiff systems, species populations may go negative. Finding an accurate time step for a system can be annoying. |
HyJCMSS Fixed Milstein | Increased accuracy. May use a larger time step. | Evaluation of 2D Itô integrals decreases speed of simulation. |
HyJCMSS Adaptive Euler-Maruyama | Automatically chooses an accurate time step, based on the SDE tolerance. | Does not always converge to the correct solution. Usage is inadvisable. Included for educational purposes only. |
HyJCMSS Adaptive Milstein | Dynamically chooses accurate time step. Increased efficiency when transient stiffness exists. With a reasonable tolerance, convergence to correct solution is guaranteed. | Slower than fixed methods for systems with constant timescales, due to the computational overhead in the adaptive code. |