Error analysis in stochastic solutions of population balance equations

Kun Zhou, Xiao Jiang, Tat Leung Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


Stochastic simulation of population balance equations (PBEs) is robust and flexible; however, it exhibits intrinsic stochastic errors which decreases at a very slow rate when increasing the computational resolution. Generally, these stochastic methods can be classified into two groups: (i) the classical Gillespie method and (ii) weighted flow algorithm. An analytical relationship is derived for the first time to connect the variances in these two groups. It also provides a detailed analysis of the resampling process, which has not been given appropriate attention previously. It is found that resampling has a profound effect on the numerical precision. Moreover, by comparing the time evolutions between systematic errors (i.e., errors in the mean value) and stochastic errors (i.e., variances), it is found that the former grows considerably faster than the latter; thus, systematic errors eventually dominate. The present findings facilitate the choice of the most suitable stochastic method for a specific PBE a priori in order to balance numerical precision and efficiency.

Original languageEnglish
Pages (from-to)531-552
Number of pages22
JournalApplied Mathematical Modelling
Publication statusPublished - Apr 2020


  • Aerosol dynamics
  • Population balance equations
  • Smoluchowski equation
  • Stochastic methods
  • Stochastic variance
  • Weighted flow algorithm

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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