Differential evolution algorithm to solve singularly perturbed problem with two small parameters

Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (4): 19-23.

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Differential evolution algorithm to solve singularly perturbed problem with two small parameters

LIU Libin1, KONG Xiangsheng2, OUYANG Aijia3，4

1.Department of Mathematics and Computer Science, Chizhou College, Chizhou, Anhui 247000, China
2.Department of Computer Engineering, Xinxiang University, Xinxiang, Henan 453000, China
3.College of Computer, Hunan Science & Technology Economy Trade Vocation College, Hengyang, Hunan 421001, China
4.College of Information Science & Engineering, Hunan City University, Yiyang, Hunan 413000, China

Online:2016-02-15 Published:2016-02-03

含两个参数的奇异摄动问题的差分进化算法

刘利斌1，孔祥盛2，欧阳艾嘉3，4

1.池州学院数学与计算机科学系，安徽池州 247000
2.新乡学院计算机与信息工程学院，河南新乡 453000
3.湖南科技经贸职业学院计算机学院，湖南衡阳 421001
4.湖南城市学院信息科学与工程学院，湖南益阳 413000

Abstract

Abstract: For using the numerical method on a Shishkin mesh to solve the singularly perturbed problem with two small parameters, based on the finite difference method, the Shishkin mesh transition parameter selection problem is transformed into an unconstrained optimization problem which is solved by using the differential evolution algorithm. It is shown from the numerical results that the accuracy of numerical solution to singularly perturbed problem on the boundary layer is improved by using the differential evolution algorithm to optimize Shishkin mesh parameters；it further verifies the feasibility and effectiveness of the proposed method.

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Key words: singularly problem, Shishkin mesh, mesh parameter, differential evolution algorithm

摘要： 针对在Shishkin网格上数值求解含有两个参数的奇异摄动问题，在有限差分方法的基础上，将Shishkin网格过渡点参数选取问题转化成一个无约束优化问题，并采用差分进化算法进行求解。数值结果表明用差分进化算法得到最优Shishkin网格参数后，奇异摄动问题的数值解在边界层的精度得到了明显的提高，进一步说明了方法的有效性和可靠性。

关键词: 奇异摄动问题, Shishkin网格, 网格参数, 差分进化算法

LIU Libin1, KONG Xiangsheng2, OUYANG Aijia3，4. Differential evolution algorithm to solve singularly perturbed problem with two small parameters[J]. Computer Engineering and Applications, 2016, 52(4): 19-23.

刘利斌1，孔祥盛2，欧阳艾嘉3，4. 含两个参数的奇异摄动问题的差分进化算法[J]. 计算机工程与应用, 2016, 52(4): 19-23.

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Differential evolution algorithm to solve singularly perturbed problem with two small parameters

含两个参数的奇异摄动问题的差分进化算法

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