奇异摄动反应扩散方程数值模拟的粒子群优化算法

doi:10.11772/j.issn.1001-9081.2014.04.1080

计算机应用 ›› 2014, Vol. 34 ›› Issue (4): 1080-1082.DOI: 10.11772/j.issn.1001-9081.2014.04.1080

奇异摄动反应扩散方程数值模拟的粒子群优化算法

刘利斌¹,欧阳艾嘉²,³

1. 池州学院数学与计算机科学系,安徽池州 247000;
2. 湖南科技经贸职业学院计算机学院,湖南衡阳 421001;
3. 湖南大学信息科学与工程学院,长沙 410082

收稿日期:2013-09-09 修回日期:2013-11-15 发布日期:2014-04-29 出版日期:2014-04-01
通讯作者: 刘利斌
作者简介:刘利斌(1982-),男,湖南娄底人,讲师,博士,主要研究方向:智能计算、微分方程数值解法;
欧阳艾嘉(1975-),男,湖南娄底人,讲师,博士,主要研究方向:智能计算。
基金资助:
国家自然科学基金资助项目;湖南省教育厅科研课题项目;安徽省优秀青年人才基金重点项目

Numerical simulation-based particle swarm optimization algorithm of singularly perturbed reaction-diffusion equation

LIU Libin¹,OUYANG Aijia²,³

1. Department of Mathematics and Computer Science, Chizhou University, Chizhou Anhui 247000, China
2. College of Computer, Hunan Science and Technology Economy Trade Vocation College, Hengyang Hunan 421001, China
3. College of Information Science and Engineering, Hunan University, Changsha Hunan 410082, China

Received:2013-09-09 Revised:2013-11-15 Online:2014-04-29 Published:2014-04-01
Contact: LIU Libin
Supported by:
National Natural Science Foundation

摘要/Abstract

摘要：

针对Shishkin网格方法在数值求解奇异摄动反应扩散方程时，网格过度点参数的选取具有不确定性的缺陷，提出了一种用粒子群优化(PSO)算法估计Shishkin网格参数的方法。首先基于有限差分方法，构造了以误差范数最小为目标的无约束优化问题，并用PSO算法进行了求解。该方法克服了人为选择参数的缺陷。实验结果表明：与单纯形算法相比，PSO算法在优化Shishkin网格参数时能够收敛到全局最优解;而且在最优网格参数下，奇异摄动反应扩散方程的数值结果在边界层的精度也得到了明显提高，进一步说明了所提方法的有效性和可行性。

Abstract:

There are some uncertainty defects of parameter selection in excessive grid points, when Shishkin mesh method is used to solve singularly perturbed reaction-diffusion equations by numerical solution. The Particle Swarm Optimization (PSO) algorithm was used to estimate the parameters of Shishkin mesh. First, based on finite difference method, an unconstrained optimization problem which was directed towards minimizing error norm was constructed. Then the PSO was used to solve it. The proposed method overcame the defects of artificial parameters selection. The experimental results show that compared with the simplex algorithm, PSO can converge to the global optimal solution for optimizing the parameters of Shishkin mesh. The accuracy of numerical computing is improved significantly for singularly perturbed reaction-diffusion equations on the boundary layer, which further illustrates the effectiveness and feasibility of the proposed method.

中图分类号:

TP18
TP301.6

刘利斌欧阳艾嘉. 奇异摄动反应扩散方程数值模拟的粒子群优化算法[J]. 计算机应用, 2014, 34(4): 1080-1082.

LIU Libin OUYANG Aijia. Numerical simulation-based particle swarm optimization algorithm of singularly perturbed reaction-diffusion equation[J]. Journal of Computer Applications, 2014, 34(4): 1080-1082.

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奇异摄动反应扩散方程数值模拟的粒子群优化算法

Numerical simulation-based particle swarm optimization algorithm of singularly perturbed reaction-diffusion equation

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