Numerical simulation of fractional Power diffusion Biosensors

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-03-21 DOI:10.3846/mma.2023.17583

Ignas Dapšys, R. Čiegis

引用次数: 0

Abstract

The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed.

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分数功率扩散生物传感器的数值模拟

本文的主要目的是为模拟生物传感器提出新的数学模型，并建立和研究离散方法来有效地求解所得到的非线性偏微分方程系统。用椭圆算子的非局部分数幂代替经典的线性扩散算子。将分裂型有限体积格式作为引入新数学模型的基本模板。因此，研究了分裂格式的精度，并与对称的Crank-Nicolson格式进行了比较。研究了近似误差与解的正则性的关系。给出了不同分数参数值下的计算实验结果并进行了分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.