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Year 2018, Volume: 3 Issue: 2, 1 - 8, 30.08.0208

Abstract

References

  • [1] N. Kurt, M. Sezer, A. C¸ elik, Solution of Dirichlet problem for a rectangular region in terms of elliptic functions, J. Comput. Math., 81, (2004), 1417-1426.
  • [2] N. Kurt, M. Sezer, Solution of Dirichlet problem for a triangle region in terms of elliptic functions, Appl.Math. Comput., 182, (2006), 73-78.
  • [3] N.Kurt, Solution of the two-dimensional heat equation for a square in terms of elliptic functions, Journal of the Franklin Institute, 345(3), (2007), 303-317.
  • [4] N. Baykus¸ Savas¸aneril, H. Delibas, Analytic solution for two-dimensional heat equation for an ellipse region. NTMSCI 4(1) (2016) 65-70.
  • [5] N. Baykus¸ Savas¸aneril, H. Delibas, Analytic Solution for The Dirichlet Problem in 2-D Journal of Computational and Theoretical Nanoscience, ACCEPTED.
  • [6] Z. Hacıoglu, N. Baykus¸ Savas¸aneril, H. K¨ose, Solution of Dirichlet problem for a square region in terms of elliptic functions, NTMSCI, 3(4), (2015), 98-103.
  • [7] E. Kurul, N. Baykus¸ Savas¸aneril, Solution of the two-dimensional heat equation for a rectangular plate, NTMSCI, 3(4), (2015), 76-82.
  • [8] M.R. Ahmadi, H. Adibi, The Chebyshev tau technique for the solution of Laplace’s equation, Applied Mathematics and Computation, 184(2), (2007), 895-900.
  • [9] W. Kong, X. Wu, Chebyshev tau matrix method for Poisson-type equations in irregular domain, Journal of Computational and Applied Mathematics, 228(1), (2009), 158-167.
  • [10] G. Y¨uksel, O.R. Is¸ık, M. Sezer, Error analysis of the Chebyshev collocation method for linear second-order partial differential equations, International Journal of Computer Mathematics, (2014), http://dx.doi.org/10.1080/00207160.2014.966099.
  • [11] G. Y¨uksel, Chebyshev polynomials solutions of second order linear partial differential equations, Ph.D. Thesis, Mugla University, Mugla, (2011).
  • [12] M. Tamsir, O. Acan, J. Kumar, A. Singh, Numerical Study of Gas Dynamics Equation arising in Shock Fronts, Asia Pacific J. Eng. Sci. Technol., 2 (2016), 17-25.
  • [13] O. Acan, O. Firat, Y. Keskin, G. Oturanc¸, Solution of Conformable Fractional Partial Differential Equations by Reduced Differential Transform Method, Selcuk J. Appl. Math., (2016) (In press).
  • [14] A. Kurnaz, G. Oturanc¸, M.E. Kiris, n-dimensional differential transformation method for solving PDEs, International Journal of Computer Mathematics, 82(3), (2005), 369-380.

Chebyshev collocation method for the two-dimensional heat equation

Year 2018, Volume: 3 Issue: 2, 1 - 8, 30.08.0208

Abstract

The purpose of this study is to apply the Chebyshev collocation method to the two- dimensional heat equation. The method
converts the two-dimensional heat equation to a matrix equation, which corresponds to a system of linear algebraic equations. Error
analysis and illustrative example is included to demonstrate the validity and applicability of the technique.

References

  • [1] N. Kurt, M. Sezer, A. C¸ elik, Solution of Dirichlet problem for a rectangular region in terms of elliptic functions, J. Comput. Math., 81, (2004), 1417-1426.
  • [2] N. Kurt, M. Sezer, Solution of Dirichlet problem for a triangle region in terms of elliptic functions, Appl.Math. Comput., 182, (2006), 73-78.
  • [3] N.Kurt, Solution of the two-dimensional heat equation for a square in terms of elliptic functions, Journal of the Franklin Institute, 345(3), (2007), 303-317.
  • [4] N. Baykus¸ Savas¸aneril, H. Delibas, Analytic solution for two-dimensional heat equation for an ellipse region. NTMSCI 4(1) (2016) 65-70.
  • [5] N. Baykus¸ Savas¸aneril, H. Delibas, Analytic Solution for The Dirichlet Problem in 2-D Journal of Computational and Theoretical Nanoscience, ACCEPTED.
  • [6] Z. Hacıoglu, N. Baykus¸ Savas¸aneril, H. K¨ose, Solution of Dirichlet problem for a square region in terms of elliptic functions, NTMSCI, 3(4), (2015), 98-103.
  • [7] E. Kurul, N. Baykus¸ Savas¸aneril, Solution of the two-dimensional heat equation for a rectangular plate, NTMSCI, 3(4), (2015), 76-82.
  • [8] M.R. Ahmadi, H. Adibi, The Chebyshev tau technique for the solution of Laplace’s equation, Applied Mathematics and Computation, 184(2), (2007), 895-900.
  • [9] W. Kong, X. Wu, Chebyshev tau matrix method for Poisson-type equations in irregular domain, Journal of Computational and Applied Mathematics, 228(1), (2009), 158-167.
  • [10] G. Y¨uksel, O.R. Is¸ık, M. Sezer, Error analysis of the Chebyshev collocation method for linear second-order partial differential equations, International Journal of Computer Mathematics, (2014), http://dx.doi.org/10.1080/00207160.2014.966099.
  • [11] G. Y¨uksel, Chebyshev polynomials solutions of second order linear partial differential equations, Ph.D. Thesis, Mugla University, Mugla, (2011).
  • [12] M. Tamsir, O. Acan, J. Kumar, A. Singh, Numerical Study of Gas Dynamics Equation arising in Shock Fronts, Asia Pacific J. Eng. Sci. Technol., 2 (2016), 17-25.
  • [13] O. Acan, O. Firat, Y. Keskin, G. Oturanc¸, Solution of Conformable Fractional Partial Differential Equations by Reduced Differential Transform Method, Selcuk J. Appl. Math., (2016) (In press).
  • [14] A. Kurnaz, G. Oturanc¸, M.E. Kiris, n-dimensional differential transformation method for solving PDEs, International Journal of Computer Mathematics, 82(3), (2005), 369-380.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sevin Gumgum

Emel Kurul This is me

Nurcan Baykus Savasaneril This is me

Publication Date August 30, 208
Published in Issue Year 2018 Volume: 3 Issue: 2

Cite

APA Gumgum, S., Kurul, E., & Baykus Savasaneril, N. Chebyshev collocation method for the two-dimensional heat equation. Communication in Mathematical Modeling and Applications, 3(2), 1-8.
AMA Gumgum S, Kurul E, Baykus Savasaneril N. Chebyshev collocation method for the two-dimensional heat equation. CMMA. 3(2):1-8.
Chicago Gumgum, Sevin, Emel Kurul, and Nurcan Baykus Savasaneril. “Chebyshev Collocation Method for the Two-Dimensional Heat Equation”. Communication in Mathematical Modeling and Applications 3, no. 2 : 1-8.
EndNote Gumgum S, Kurul E, Baykus Savasaneril N Chebyshev collocation method for the two-dimensional heat equation. Communication in Mathematical Modeling and Applications 3 2 1–8.
IEEE S. Gumgum, E. Kurul, and N. Baykus Savasaneril, “Chebyshev collocation method for the two-dimensional heat equation”, CMMA, vol. 3, no. 2, pp. 1–8.
ISNAD Gumgum, Sevin et al. “Chebyshev Collocation Method for the Two-Dimensional Heat Equation”. Communication in Mathematical Modeling and Applications 3/2, 1-8.
JAMA Gumgum S, Kurul E, Baykus Savasaneril N. Chebyshev collocation method for the two-dimensional heat equation. CMMA.;3:1–8.
MLA Gumgum, Sevin et al. “Chebyshev Collocation Method for the Two-Dimensional Heat Equation”. Communication in Mathematical Modeling and Applications, vol. 3, no. 2, pp. 1-8.
Vancouver Gumgum S, Kurul E, Baykus Savasaneril N. Chebyshev collocation method for the two-dimensional heat equation. CMMA. 3(2):1-8.