A New Constructing Rational Functions Method For Solving Lane-Emden Type Equations

被引：3
|
作者：
He, Jilong [1 ]
Zheng, Zhoushun [1 ]
Du, Changfa [1 ]
机构：
[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
NEURAL PROCESSING LETTERS | 2023年 / 55卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Rational Chebyshev polynomials; Lane-Emden equation; Error back propagation algorithm; Machine learning; NEURAL-NETWORK; NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; COLLOCATION APPROACH; WAVELETS METHOD; ALGORITHM; PHYSICS; MODEL;
D O I：
10.1007/s11063-022-10968-6
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, a new construction machine learning method is proposed based on Rational Chebyshev polynomials to solve Lane-Emden type differential equations. The method is used for training, and the parameters are obtained by the error back propagation principle. By comparing with Chebyshev neural network proposed in [Appl. Math. Comp. 247:100-114(2014)][Appl. Soft. Comp. 43:347-356(2016)], our results are more accurate.
引用
收藏
页码：1889 / 1918
页数：30
相关论文
共 50 条
  • [1] A New Constructing Rational Functions Method For Solving Lane−Emden Type Equations
    Jilong He
    Zhoushun Zheng
    Changfa Du
    Neural Processing Letters, 2023, 55 : 1889 - 1918
  • [2] ULTRASPHERICAL WAVELETS METHOD FOR SOLVING LANE-EMDEN TYPE EQUATIONS
    Youssri, Y. H.
    Abd-Elhameed, W. M.
    Doha, E. H.
    ROMANIAN JOURNAL OF PHYSICS, 2015, 60 (9-10): : 1298 - 1314
  • [3] Laguerre collocation method for solving Lane-Emden type equations
    Zamiri, Ali
    Borhanifar, Abdollah
    Ghannadiasl, Amin
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2021, 9 (04): : 1176 - 1197
  • [4] Solution of Lane-Emden type equations using rational Bernoulli functions
    Calvert, Velinda
    Mashayekhi, Somayeh
    Razzaghi, Mohsen
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (05) : 1268 - 1284
  • [5] A new algorithm for solving differential equations of Lane-Emden type
    Wazwaz, AM
    APPLIED MATHEMATICS AND COMPUTATION, 2001, 118 (2-3) : 287 - 310
  • [6] Legendre wavelets method for solving differential equations of Lane-Emden type
    Yousefi, Sohrab Ali
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (02) : 1417 - 1422
  • [7] A numerical method for solving singular fractional Lane-Emden type equations
    Nasab, A. Kazemi
    Atabakan, Z. Pashazadeh
    Ismail, A. I.
    Ibrahim, Rabha W.
    JOURNAL OF KING SAUD UNIVERSITY SCIENCE, 2018, 30 (01) : 120 - 130
  • [8] Differential transformation method for solving differential equations of Lane-emden type
    Ertürk, Vedat Suat
    Mathematical and Computational Applications, 2007, 12 (03) : 135 - 139
  • [9] NEW GALERKIN OPERATIONAL MATRICES FOR SOLVING LANE-EMDEN TYPE EQUATIONS
    Abd-Elhameed, W. M.
    Doha, E. H.
    Saad, A. S.
    Bassuony, M. A.
    REVISTA MEXICANA DE ASTRONOMIA Y ASTROFISICA, 2016, 52 (01) : 83 - 92
  • [10] Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type
    Parand, K.
    Shahini, M.
    Dehghan, Mehdi
    JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (23) : 8830 - 8840
12345