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An overview of the Hy3S numerical methods |
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| Name |
Advantages |
Disadvantages |
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| 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. |
Salis et al. BMC Bioinformatics 2006 7:93 doi:10.1186/1471-2105-7-93 |
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