### Abstract

We propose an efficient and accurate numerical scheme for solving probability generating functions arising in stochastic models of general first-order reaction networks by using the characteristic curves. A partial differential equation derived by a probability generating function is the transport equation with variable coefficients. We apply the idea of characteristics for the estimation of statistical measures, consisting of the mean, variance, and marginal probability. Estimation accuracy is obtained by the Newton formulas for the finite difference and time accuracy is obtained by applying the fourth order Runge-Kutta scheme for the characteristic curve and the Simpson method for the integration on the curve. We apply our proposed method to motivating biological examples and show the accuracy by comparing simulation results from the characteristic method with those from the stochastic simulation algorithm.

Original language | English |
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Pages (from-to) | 316-337 |

Number of pages | 22 |

Journal | Journal of Mathematical Chemistry |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- Characteristic method
- First-order partial differential equation
- First-order reaction network
- Monte Carlo method

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics