Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (17): 225-230.DOI: 10.3778/j.issn.1002-8331.1711-0397

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Differential evolution and rational spectral methods for singularly perturbed problems

LIU Libin1,2, LONG Guangqing1,2, SHANGGUAN Zhenping1   

  1. 1.School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530023, China
    2.Guangxi Colleges and Universities Key Laboratory of Data Science, Nanning 530023, China
  • Online:2018-09-01 Published:2018-08-30



  1. 1.广西师范学院 数学与统计科学学院,南宁 530023
    2.广西高校数据科学重点实验室,南宁 530023

Abstract: This paper discusses a high precision rational spectral collocation method for singularly perturbed problems. Using the rational spectral collocation method with sinh transformation, the Chebyshev nodes are encrypted at the boundary layer, and the higher precision can be achieved with fewer nodes. Then, in order to obtain the width of boundary layer in the sinh transformation, it designs an unconstrained nonlinear optimization problem with the least error as the objective function, and gives the differential evolution algorithm to solve this optimization problem.

Key words: sinh transformation, rational spectral collocation method, singularly perturbed, differential evolution algorithm

摘要: 讨论一种数值求解奇异摄动问题的高精度有理谱配点法。用sinh变换的有理谱配点法使Chebyshev节点在边界层处加密,只需较少的节点即可达到较高的精度。为了获得sinh变换中边界层的宽度,设计了一个以误差最小为目标函数的无约束的非线性优化问题,并给出了求解该优化问题的差分进化算法。数值实验表明,与其他的智能算法和传统的优化算法相比,差分进化算法在sinh变换中的参数优化方面具有明显的优势。

关键词: sinh变换, 有理谱配点法, 奇异摄动, 差分进化算法