• 论文 • 上一篇
黄英杰, 周凤英, 许小勇
黄英杰, 周凤英, 许小勇. 第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程[J]. 数值计算与计算机应用, 2023, 44(1): 95-112.
Huang Yingjie, Zhou Fengying, Xu Xiaoyong. USING THE SIXTH KIND OF ORTHOGONAL CHEBYSHEV POLYNOMIAL MIXED BLOCK PULSE FUNCTION TO SOLVE FRACTIONAL LANE-EMDEN DIFFERENTIAL EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 95-112.
Huang Yingjie, Zhou Fengying, Xu Xiaoyong
MR(2010)主题分类:
分享此文:
[1] Chandrasekhar S. An Introduction to the Study of Stellar Structure[M]. NewYork:Dover Publi cations, 1967. [2] Richardson O U. The Emission of Electricity From Hot Bodies[M]. London:Longmans Green and Company, 1921. [3] Sahu P K, Saha R S. Two-dimensional Legendre wavelet method for the numerical solutions of fuzzy integro-differential equations[J]. Journal of Intelligent and Fuzzy Systems, 2015, 28(3):1271-1279. [4] Nouh M I, Abdel-Salam E A B. Approximate Solution to the Fractional Lane-Emden Type Equations[J]. Iran J Sci Technol Trans Sci, 2018, 42:2199-2206. [5] Randhir S, Himanshu G, Vandana G. Haar wavelet collocation method for Lane-Emden equations with Dirichlet, Neumann and Neumann-Robin boundary conditions[J]. Journal of Computational Applied Mathematics, 2019, 346:150-161. [6] Roul P, Kumari T, Goura V M K P. An efficient numerical approach for solving a general class of nonlinear singular boundary value problems[J]. Journal of Mathematical Chemistry, 2021, 59:1977-1993. [7] Mahboubeh M A, Zahra S. Application of Compact Finite Difference Method for Solving Some Type of Fractional Derivative Equations[J]. International Journal of Circuits, Systems and Signal Processing, 2021, 15(143):1324-1335. [8] Zhang B, Tang Y, Zhang X. Numerical solution of fractional differential equations using hybrid Bernoulli polynomials and block pulse functions[J]. Math Sci., 2021, 15:293-304. [9] Meng Z J, Yi M X, Huang J. Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials[J]. Applied Mathematics and Computation, 2018, 336:454-464. [10] Haider A M, Tahrier N. New Algorithm of the Optimal Homotopy Asymptotic Method for Solving Lane-Emden Equations[J]. Journal of Applied Mathematics and Computation, 2021, 5(4):237-246. [11] Delkhosh M, Rahmanzadeh A, Shafiei S F. Solving nonlinear differential equations in astrophysics and fluid mechanics using the generalized pseudo spectral method[J]. SeMA, 2021, 78:457-474. [12] Parand K, Mehdi D, Rezaei A R. An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method[J]. Computer Physics Communications, 2010, 181(6):1096-1108. [13] Mirshafiee S, Kajani M T, Goughery H S. Numerical solving of nonlinear differential equations using a hybrid method on a semi-infinite interval[J]. Comp. Appl. Math., 2021, 40:284. [14] Parand K, Hashemi S. RBF-DQ method for solving non-linear differential equations of LaneEmden type[J]. Ain Shams Engineering Journal, 2018, 9(4):615-629. [15] Youssri Y H, Elhameed A W M, Doha E H. Ultraspherical wavelets method for solving LaneEmden type equations[J]. Rom. J. Phys, 2015, 60(9):1298-1314. [16] Abdelhalim E. A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method[J]. Journal of Computational and Applied Mathematics, 2010, 235(8):1914-1924. [17] Zhou F Y, Xu X Y. The third kind Chebyshev wavelets collocation method for solving the timefractional convection diffusion equations with variable coefficients[J].Applied Mathematics and Computation, 2016, 280:11-29 [18] 张元林,工程数学积分变换(第四版)[M].北京:高等教育出版社, 2003, 67-139. [19] Marzban H R, Malakoutikhah F. Solution of delay fractional optimal control problems using a hybrid of block-pulse functions and orthonormal Taylor polynomials[J]. Journal of the Franklin Institute, 2019, 356(15):8182-8215. [20] Sahu P K, Ray S. Hybrid Legendre Block-Pulse functions for the numerical solutions of system of nonlinear Fredholm-Hammerstein integral equations[J].Applied Mathematics and Computation, 2015, 270:871-878. [21] Abd-Elhameed W M, Youssri Y H. Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations[J]. Comp. Appl. Math., 2018, 37(3):2897-2921. [22] Charles F D,Yuan X. Orthogonal Polynomials in Several Varaibles[M]. Cambridge University Press, 2001, Ch1.5.2. [23] Kilicman A, Zhour Z A A A. Kronecker operational matrices for fractional calculus and some applications[J]. Applied Mathematics and Computation, 2007, 187(1):250-265. [24] Zhou F Y, Xu X Y. Numerical solutions for the linear and nonlinear singular boundary value problems using Laguerre wavelets[J]. Adv Differ Equ., 2016, 2016:17. [25] Kazemi N A, Pashazadeh A Z. A numerical method for solving singular fractional Lane-Emden type equations[J]. Journal of King Saud University-Science, 2018, 30(1):120-130. [26] Saadatmandi A, Ghasemi N A, Eftekhari A. Numerical study of singular fractional Lane-Emden type equations arising in astrophysics[J]. J Astrophys Astron, 2019, 40. doi:10.1007/s12036-019-9587-0 |
[1] | 张继伟. 非局部和反常扩散模型的数值方法[J]. 数值计算与计算机应用, 2021, 42(3): 183-214. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||