差分进化算法在奇异摄动问题数值模拟中的应用  

The Application of Differential Evolution Algorithm in Numerical Simulation of Singularly Perturbed Problem

作　　者：包小兵[1] BAO Xiaobing(Department of Mathematics and Computer Science, Chizhou College, Chizhou, Anhui 247000, China)

机构地区：[1]池州学院数学与计算机学院,安徽池州247000

出　　处：《铜仁学院学报》2017年第3期107-111,共5页Journal of Tongren University

基　　金：池州学院院级自然项目(2014ZR005)

摘　　要：针对在Shishkin网格上数值求解含内点层的奇异摄动问题,在迎风有限差分格式的基础上,提出了一种基于差分进化算法的Shishkin网格参数估计方法。利用该方法可计算出最优的Shishkin网格参数,同时获得了相应的数值结果。数值实验表明差分进化算法具有很好的全局寻优能力和较快的收敛速度,能有效解决传统迭代优化算法对初值的依赖问题。For using the numerical method on a Shishkin mesh to solve the singularly perturbed problem with an interior layer, based on the finite difference method, a parameter estimation method for Shishkin mesh based on Differential Evolution algorithm is presented. This approach is applied to calculate the best Shishkin mesh parameter,and the corresponding numerical results. It is shown from the numerical results that the Differential Evolution algorithm has the capabilities of global optimization and the faster convergence rate. It is more independent of initial value than the traditional ones.

关 键 词：差分进化算法 奇异摄动 参数估计 SHISHKIN网格 

分 类 号：O241[理学—计算数学] TP18[理学—数学]