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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.