A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations

被引：4
|
作者：
Idiz, Fatih [1 ]
Tanoglu, Gamze [1 ]
Aghazadeh, Nasser [1 ]
机构：
[1] Izmir Inst Technol, Dept Math, Izmir, Turkiye
来源：
NUMERICAL ALGORITHMS | 2024年 / 95卷 / 01期
关键词：
Legendre wavelet; Lane-Emden equation; Fractional differential equation; Quasilinearization; PARTIAL-DIFFERENTIAL-EQUATIONS; GALERKIN METHOD;
D O I：
10.1007/s11075-023-01568-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature.
引用
收藏
页码：181 / 206
页数：26
相关论文
共 50 条
  • [1] A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations
    Fatih İdiz
    Gamze Tanoğlu
    Nasser Aghazadeh
    [J]. Numerical Algorithms, 2024, 95 : 181 - 206
  • [2] A numerical method for solving singular fractional Lane-Emden type equations
    Nasab, A. Kazemi
    Atabakan, Z. Pashazadeh
    Ismail, A. I.
    Ibrahim, Rabha W.
    [J]. JOURNAL OF KING SAUD UNIVERSITY SCIENCE, 2018, 30 (01) : 120 - 130
  • [3] Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
    Ali Akgül
    Mustafa Inc
    Esra Karatas
    Dumitru Baleanu
    [J]. Advances in Difference Equations, 2015
  • [4] Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
    Akgul, Ali
    Inc, Mustafa
    Karatas, Esra
    Baleanu, Dumitru
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2015,
  • [5] Legendre wavelets method for solving differential equations of Lane-Emden type
    Yousefi, Sohrab Ali
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (02) : 1417 - 1422
  • [6] Numerical Solution to Singular Ordinary Differential Equations of Lane-Emden Type By Legendre Collocation Method
    Zhao, T. G.
    Wu, Y.
    [J]. PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATERIAL ENGINEERING AND APPLICATION (ICMEA 2016), 2016, 103 : 496 - 501
  • [7] An efficient technique based on higher order Haar wavelet method for Lane-Emden equations
    Swati
    Singh, Mandeep
    Singh, Karanjeet
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 206 : 21 - 39
  • [8] Approximate Solution to the Fractional Lane-Emden Type Equations
    Nouh, M. I.
    Abdel-Salam, Emad A. -B.
    [J]. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2018, 42 (A4): : 2199 - 2206
  • [9] A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane-Emden equations
    Dizicheh, A. Karimi
    Salahshour, S.
    Ahmadian, A.
    Baleanu, D.
    [J]. APPLIED NUMERICAL MATHEMATICS, 2020, 153 (153) : 443 - 456
  • [10] Numerical study of singular fractional Lane-Emden type equations arising in astrophysics
    Saadatmandi, Abbas
    Ghasemi-Nasrabady, Azam
    Eftekhari, Ali
    [J]. JOURNAL OF ASTROPHYSICS AND ASTRONOMY, 2019, 40 (03)
12345