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Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods

    Authors

    • Fatemeh Baharifard 1
    • Kourosh Parand 2

    1 School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    2 Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

,

Document Type : Regular paper

10.52547/CMCMA.1.1.69
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Abstract

In this paper, we apply the collocation method for solving some classes of Lane-Emden type equations that are determined in interval $[0, 1]$ and semi-infinite domain. We use an orthogonal system of functions, namely Gegenbauer polynomials and introduce the shifted Gegenbauer polynomials and the rational Gegenbauer functions as basis functions in the collocation method for problems in interval $[0, 1]$ and semi-infinite domain, respectively.
We estimate that the proposed method has super-linear convergence rate
and also investigate the Gegenbauer parameter $ (\alpha)$ to get more accurate answers for various Lane-Emden type problems. The comparison between the proposed method and other numerical results shows that the method is efficient and applicable. 

Keywords

  • Gegenbauer polynomials
  • Rational Gegenbauer functions
  • Collocation method
  • Nonlinear ODE
  • Lane-Emden equations
  • Astrophysics
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 69-85
Files
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  • PDF 340.91 K
History
  • Receive Date: 12 May 2023
  • Revise Date: 31 May 2023
  • Accept Date: 30 June 2023
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
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Statistics
  • Article View: 73
  • PDF Download: 323

APA

Baharifard, F. and Parand, K. (2022). Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), 69-85. doi: 10.52547/CMCMA.1.1.69

MLA

Baharifard, F. , and Parand, K. . "Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 1, 2022, 69-85. doi: 10.52547/CMCMA.1.1.69

HARVARD

Baharifard, F., Parand, K. (2022). 'Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), pp. 69-85. doi: 10.52547/CMCMA.1.1.69

CHICAGO

F. Baharifard and K. Parand, "Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 1 (2022): 69-85, doi: 10.52547/CMCMA.1.1.69

VANCOUVER

Baharifard, F., Parand, K. Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(1): 69-85. doi: 10.52547/CMCMA.1.1.69

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