Highly accurate tau-leaping methods with random corrections.

Area of Science:

• Computational Chemistry
• Applied Mathematics
• Chemical Kinetics

Background:

• Stochastic chemical kinetic systems require accurate numerical simulation methods.
• Existing tau-leaping methods have limitations in local truncation error, affecting accuracy.
• Higher-order methods are needed for precise simulation of chemical reactions.

Purpose of the Study:

• To construct higher-order tau-leaping methods for simulating stochastic chemical kinetic systems.
• To improve the accuracy of tau-leaping approximations by reducing local truncation error.
• To develop novel numerical techniques for simulating jump processes.

Main Methods:

• Introducing random corrections (Poisson or Gaussian) to the primitive tau-leaping scheme.
• Analyzing the reduction in local truncation error for mean and covariance.
• Implementing and testing novel Poisson and Gaussian random correction tau-leaping methods.

Main Results:

• The Poisson random correction method reduces local truncation error for the mean to O(tau(3)).
• Gaussian random correction methods reduce local truncation error for both mean and covariance to O(tau(3)).
• Numerical results show improved accuracy in capturing mean and variance compared to existing methods.

Conclusions:

• Novel random correction tau-leaping methods significantly enhance accuracy for chemical reaction system simulation.
• These methods provide a viable approach for accurate and efficient simulation of stochastic chemical kinetics.
• This work is a foundational step towards advanced numerical methods for jump processes.