氡测度空间中尺寸结构凝聚-破碎模型的高分辨率有限差分格式。

High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures.

作者信息

Ackleh Azmy S, Lyons Rainey, Saintier Nicolas

机构信息

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA.

Department of Mathematics and Computer Science, Karlstad University, 651 88 Karlstad, Sweden.

出版信息

Math Biosci Eng. 2023 May 9;20(7):11805-11820. doi: 10.3934/mbe.2023525.

DOI:10.3934/mbe.2023525

PMID:37501421

Abstract

In this paper, we develop explicit and semi-implicit second-order high-resolution finite difference schemes for a structured coagulation-fragmentation model formulated on the space of Radon measures. We prove the convergence of each of the two schemes to the unique weak solution of the model. We perform numerical simulations to demonstrate that the second order accuracy in the Bounded-Lipschitz norm is achieved by both schemes.

摘要

在本文中，我们针对在拉东测度空间上构建的结构化凝聚 - 破碎模型，开发了显式和半隐式二阶高分辨率有限差分格式。我们证明了这两种格式中的每一种都收敛于该模型的唯一弱解。我们进行了数值模拟，以证明这两种格式在有界 - 利普希茨范数下均达到二阶精度。