Corpus ID: 235458360

Optimal explicit stabilized postprocessed τ-leap method for the simulation of chemical kinetics

@article{Abdulle2021OptimalES,
  title={Optimal explicit stabilized postprocessed $\tau$-leap method for the simulation of chemical kinetics},
  author={A. Abdulle and Lia Gander and Giacomo Rosilho de Souza},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.09339}
}
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this paper we propose a new discrete stochastic simulation algorithm: the postprocessed second kind stabilized orthogonal τ -leap Runge–Kutta method (PSK-τ -ROCK). In the context of chemical kinetics this method can be seen as a stabilization of… Expand

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References

SHOWING 1-10 OF 49 REFERENCES
Slow-scale split-step tau-leap method for stiff stochastic chemical systems
TLDR
A splitting heuristic which helps to resolve some of the issues of intrinsically stiff biochemical systems and is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. Expand
Multilevel hybrid split-step implicit tau-leap
TLDR
An efficient Multilevel Monte Carlo (MLMC) method that uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues is proposed. Expand
Approximate accelerated stochastic simulation of chemically reacting systems
The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent majorExpand
Integral tau methods for stiff stochastic chemical systems.
TLDR
The implicit Minkowski-Weyl tau (IMW-τ) methods are introduced and it is shown that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. Expand
Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates.
TLDR
An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed which amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA). Expand
Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes
Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochasticExpand
Reversible-equivalent-monomolecular tau: A leaping method for "small number and stiff" stochastic chemical systems
TLDR
A new explicit leaping scheme is proposed, reversible-equivalent-monomolecular tau (REMM-?), which shows considerable promise in the simulation of "small number and stiff" systems, i.e. systems whose dynamics involve different time scales and have some molecular species present in very small numbers. Expand
A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions
Abstract An exact method is presented for numerically calculating, within the framework of the stochastic formulation of chemical kinetics, the time evolution of any spatially homogeneous mixture ofExpand
Explicit time integration of the stiff chemical Langevin equations using computational singular perturbation.
TLDR
A stable explicit time-scale splitting algorithm for stiff chemical Langevin equations (CLEs) is developed, based on the concept of computational singular perturbation, which allows time integration step sizes much larger than those required by typical explicit numerical methods for stiff stochastic differential equations. Expand
Binomial distribution based tau-leap accelerated stochastic simulation.
TLDR
Simulations using prototype reaction networks show that the BD-tau method is more accurate than the original method for comparable coarse-graining in time, and thus conserve mass. Expand
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