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A weak second order tau-leaping method for chemical kinetic systems.

Yucheng Hu1, Tiejun Li, Bin Min

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This study extends a method for chemical Langevin equations to discrete chemical jump processes, achieving higher accuracy for large systems. The new approach offers a robust and performant option for simulating discrete chemical kinetics.

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Area of Science:

  • Computational Chemistry
  • Stochastic Processes
  • Chemical Kinetics

Background:

  • Chemical Langevin equations model continuous approximations of chemical systems.
  • Existing methods like Euler and midpoint τ-leaping have limitations in accuracy for discrete processes.
  • Accurate simulation of discrete chemical kinetics is crucial for understanding complex reaction systems.

Purpose of the Study:

  • To extend the Anderson-Mattingly method to discrete chemical jump processes.
  • To achieve weak second-order accuracy for discrete chemical kinetic systems in the large volume limit.
  • To develop a more accurate and performant τ-leaping scheme for chemical reaction systems.

Main Methods:

  • Modification of the Anderson-Mattingly method for discrete chemical jump processes.
  • Analysis of convergence and numerical stability for the proposed method.
  • Numerical simulations comparing the new method with existing τ-leaping schemes.

Main Results:

  • The extended method achieves weak second-order accuracy for discrete chemical kinetic systems.
  • The local truncation error for covariance is of order τ(3)V(-1) under specific scaling conditions.
  • The proposed method demonstrates higher accuracy than Euler and midpoint τ-leaping methods.

Conclusions:

  • The new method is a promising candidate for highly accurate τ-leaping schemes.
  • The method is easy to implement and exhibits good performance.
  • This work advances the simulation capabilities for discrete chemical reaction systems.