消毒剂溶液表面去污数学模型求解的几种数值方法及比较

IF 0.3 Q4 MATHEMATICS Matematika Pub Date : 2018-12-02 DOI:10.11113/MATEMATIKA.V34.N2.1055
Chai Jin Sian, Y. Hoe, A. H. Murid
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引用次数: 0

摘要

考虑了一个数学模型来确定消毒剂溶液对表面去污的有效性。去污过程包括细菌向消毒剂溶液中的扩散和消毒剂杀灭效果的反应。数学模型是一种反应扩散型。采用有限差分法和四阶龙格-库塔线法对模型进行了数值求解。为了获得稳定的解,采用冯-诺依曼稳定性分析来评估有限差分法的稳定性。对于刚性问题,采用Dormand-Prince方法作为四阶龙格-库塔方法的估计误差。数值解的计算选用MATLAB编程。结果表明,四阶龙格-库塔法在求解消毒液模型时,与有限差分法相比,具有更大的稳定域和更好的求解精度。此外,还进行了数值模拟,研究了不同厚度的消毒液对细菌减少的影响。结果表明,浓消毒液能够更有效地降低无量纲细菌浓度
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Some Numerical Methods and Comparisons for Solving Mathematical Model of Surface Decontamination by Disinfectant Solution
A mathematical model is considered to determine the effectiveness of disinfectant solution for surface decontamination. The decontamination process involved the diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing effect. The mathematical model is a reaction-diffusion type. Finite difference method and method of lines with fourth-order Runge-Kutta method are utilized to solve the model numerically. To obtain stable solutions, von Neumann stability analysis is employed to evaluate the stability of finite difference method. For stiff problem, Dormand-Prince method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB programming is selected for the computation of numerical solutions. From the results obtained, fourth-order Runge-Kutta method has a larger stability region and better accuracy of solutions compared to finite difference method when solving the disinfectant solution model. Moreover, a numerical simulation is carried out to investigate the effect of different thickness of disinfectant solution on bacteria reduction. Results show that thick disinfectant solution is able to reduce the dimensionless bacteria concentration more effectively
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来源期刊
Matematika
Matematika MATHEMATICS-
自引率
25.00%
发文量
0
审稿时长
24 weeks
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