摘要
讨论了奇异摄动反应扩散方程的重心有理谱配置法。首先将Chebyshev配置点进行sinh变换,使更多的配置点聚集在两端边界层处。然后,为了进一步计算出边界层的宽度,构造了一个以绝对误差最小为目标函数的无约束非线性优化问题,并给出了该优化问题的自适应差分进化算法。数值实验表明,自适应差分进化算法对sinh变化的参数优化方面具有显著的优势。
In this paper,a barycentric rational spectral collocation method for singularly perturbed reaction-diffusion equation is discussed. At first,by using sinh transform,more Chebyshev points are mapped into the transformed ones clustered near the two boundary layers of the solution. Then,to calculate the widths of boundary layers in sinh transform,we construct an unconstrained nonlinear optimization problem with absolute error as the objective function,and give a self-adaptive differential evolutionary algorithm to solve this optimization problem. Finally,it is shown from the numerical experiments that the self-adaptive differential evolutionary algorithm has obvious advantages in parameter optimization of sinh transform.
作者
张健
方虹淋
刘利斌
ZHANG Jian;FANG Honglin;LIU Libin(School of Mathematics and Statistical,Nanning Normal University,Nanning 530299,China)
出处
《重庆理工大学学报（自然科学）》
CAS
北大核心
2020年第5期238-244,共7页
Journal of Chongqing University of Technology：Natural Science
基金
国家自然科学基金项目(11761015)
国家自然科学基金数学天元基金资助项目(11826211,11826212)
广西自然科学基金项目(2017GXNSFBA198183)
广西高校中青年教师基础能力提升项目(2018KY1251)。
关键词
sinh变换
重心有理谱配置法
非线性优化
奇异摄动
自适应差分进化算法
sinh transform
barycentric rational spectral collocation method
nonlinear optimization
singular perturbation
self-adaptive differential evolutionary algorithm
