High-order WENO scheme for Polymerization-type equations

TL;DR

This paper introduces a high-order WENO numerical scheme for polymerization-type equations, specifically modeling protein aggregation, ensuring mass conservation and enabling accurate simulation of the process.

Contribution

The paper develops a fifth-order WENO scheme tailored for polymerization equations, preserving mass and improving solution accuracy over existing methods.

Findings

The scheme accurately conserves total mass over time.

It achieves high-order accuracy in numerical simulations.

The method effectively models protein polymerization dynamics.

Abstract

Polymerization of proteins is a biochimical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The fifth-order WENO scheme is built to preserve the total mass of proteins along time.