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

Azmy S. Ackleh; Rainey Lyons; Nicolas Saintier; Azmy S. Ackleh; Rainey Lyons; Nicolas Saintier

doi:10.3934/mbe.2023525

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11805-11820. doi: 10.3934/mbe.2023525

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

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA
2.
Department of Mathematics and Computer Science, Karlstad University, 651 88 Karlstad, Sweden
3.
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (1428) Pabellón I - Ciudad Universitaria - Buenos Aires - ARGENTINA

Received: 24 March 2023 Revised: 19 April 2023 Accepted: 24 April 2023 Published: 09 May 2023

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.
Citation: Azmy S. Ackleh, Rainey Lyons, Nicolas Saintier. High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11805-11820. doi: 10.3934/mbe.2023525

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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.

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