Analysis of Particle Methods for Structured Population Models with Nonlocal Boundary Term in the Framework of Bounded Lipschitz Distance

作者：Gwiazda Piotr; Jablonski Jedrzej; Marciniak Czochra Anna^*; Ulikowska Agnieszka

来源：Numerical Methods for Partial Differential Equations, 2014, 30(6): 1797-1820.

DOI：10.1002/num.21879

• bounded Lipschitz distance
• Escalator Boxcar Train
• flat metric
• measure-valued solutions
• particle method
• positive Radon measures
• structured population model

Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool to study numerical schemes based on particle methods. The approach is based on the idea of tracing growth and transport of measures which approximate the solution of original partial differential equation. In this article, we present analytical and numerical study of two versions of Escalator Boxcar Train algorithm which has been widely applied in theoretical biology, and compare it to the recently developed split-up algorithm. The novelty of this article is in showing well-posedness and convergence rates of the schemes using the concept of semiflows on metric spaces. Theoretical results are validated by numerical simulations of test cases, in which distances between simulated and exact solutions are computed using flat metric.

• 出版日期2014-11