Research Article

Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation

Volume: 1 Number: 4 December 20, 2018
EN

Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation

Abstract

In this study, finite element method (FEM) with Galerkin Formula is applied to find the numerical solution of a time-dependent heat-like Lane-Emden equation. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of equation. The results indicate that Galerkin method is effectively implemented. It is seen that results are compatible with exact solutions and consistent with other existing numerical methods.

Keywords

Time-dependent Lane-Emden equation,Galerkin method,Heat-type equation,Time-dependent Lane-Emden equation

References

  1. [1] N. T. Shawagfeh, Nonperturbative approximate solution for Lane-Emden equation, J. Math. Phys., 34(9) (1993), 43–64.
  2. [2] A. M. Wazwaz Analytical solution for the time-dependent Emden–Fowler type of equations by Adomian decomposition method, Appl. Math. Comput., 166 (2005), 638–651.
  3. [3] B. Batiha, M. S. M. Noorani Application of variational iteration method to heat- and wave-like equations, Phys. Lett. A, 369 (2007), 55–61.
  4. [4] H. Caglar, M. F. Ucar, Non-polynomial spline method for a time dependent heat-like Lane-Emden equation, Acta Phys. Polon. A., 121 1 (2012), 262–264.
  5. [5] J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Internat. J. Non-Linear Mech., 34 (1999), 699–708.
  6. [6] M. S. H. Chowdhury, I. Hashim, Solutions of time-dependent Emden–Fowler type equations by homotopy-perturbation method, Phys. Lett. A, 368 (2007), 305–313.
  7. [7] S. Momani, Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method, Appl. Math. Comput., 165 (2005), 459–472.
APA
Uçar, M. F. (2018). Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation. Universal Journal of Mathematics and Applications, 1(4), 258-261. https://doi.org/10.32323/ujma.406335
AMA
1.Uçar MF. Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation. Univ. J. Math. Appl. 2018;1(4):258-261. doi:10.32323/ujma.406335
Chicago
Uçar, Mehmet Fatih. 2018. “Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation”. Universal Journal of Mathematics and Applications 1 (4): 258-61. https://doi.org/10.32323/ujma.406335.
EndNote
Uçar MF (December 1, 2018) Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation. Universal Journal of Mathematics and Applications 1 4 258–261.
IEEE
[1]M. F. Uçar, “Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 258–261, Dec. 2018, doi: 10.32323/ujma.406335.
ISNAD
Uçar, Mehmet Fatih. “Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation”. Universal Journal of Mathematics and Applications 1/4 (December 1, 2018): 258-261. https://doi.org/10.32323/ujma.406335.
JAMA
1.Uçar MF. Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation. Univ. J. Math. Appl. 2018;1:258–261.
MLA
Uçar, Mehmet Fatih. “Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, Dec. 2018, pp. 258-61, doi:10.32323/ujma.406335.
Vancouver
1.Mehmet Fatih Uçar. Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation. Univ. J. Math. Appl. 2018 Dec. 1;1(4):258-61. doi:10.32323/ujma.406335