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APPLICATION OF NEW ITERATIVE ALGORITHM FOR SOLVING NONLINEAR CONVECTION-DIFFUSION HEAT EQUATION WITH CONSTANT COEFFICIENTS

Yıl 2021, Cilt: 7 Sayı: 1, 11 - 23, 30.06.2021
https://doi.org/10.51477/mejs.801367

Öz

This paper presents computational procedures to formulate an algorithm based on the new iterative method (NIM) for the numerical solution of nonlinear convection-diffusion heat equation with constant coefficients. The newly formulated algorithm (NIA) was fully described the relationship between convection and diffusion constants. Three test cases (prototype) are consider to investigate the time distribution profiles in heat equation other study. The algorithm is easy and efficient to solve similar problems in physical sciences.

Teşekkür

Best regards sir.

Kaynakça

  • [1] M. C. Methods, Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning, EMAp, Fund. Getulio Vargas, Rio Janeiro, Brazil, vol. I, 2019 . [2] S. G. Ahmed, A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients, pp. 1–7, 2012.
  • [3] R. Kragler, Solution of 1d / 2d Advection-Diffusion Equation Using the Method of Inverse Differential Operators (MIDO), weingarten.de/web/kragler/mathematica October 2015.
  • [4] A. Kumar, D. K. Jaiswal, and N. Kumar, Analytical solutions of one-dimensional advection – diffusion equation with variable coefficients in no. 5, pp. 539–549, 2009.
  • [5] N. M. Abbasi, Analytical solution to diffusion-convection PDE in 1D, no. 2, pp. 1–7, 2019.
  • [6] D. K. Jaiswal, A. Kumar, and R. R. Yadav, Analytical Solution to the One-Dimensional Advection Diffusion Equation with Temporally Dependent Coefficients, vol. 2011, no. January, pp. 76–84, 2011.
  • [7] J. Biazar and H. Ghazvini, Homotopy perturbation method for solving hyperbolic partial differential equations, Comput. Math. with Appl., vol. 56, no. 2, pp. 453–458, 2008.
  • [8] M. Dehghan, On the Numerical Solution of the One-Dimensional Convection-Diffusion Equation, Vol. 2, No. July 2004, Pp. 61–74, 2005.
  • [9] M. Yaseen and M. Samraiz, The Modified New Iterative Method for Solving Linear and Nonlinear Klein Gordon Equations New Iterative Method [2],” vol. 6, no. 60, pp. 2979–2987, 2012.
  • [10] R. Behl, A. Cordero, and J. R. Torregrosa, New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns, pp. 1–17, 2018.
  • [11] A. Mathematics, S. Bhalekar, and V. Gejji, “New Iterative Method : Application to Partial Differential Equations,” no. September 2008, 2019.
  • [12] C. Chun, “A new iterative method for solving nonlinear equations,” vol. 178, pp. 415–422, 2006.
Yıl 2021, Cilt: 7 Sayı: 1, 11 - 23, 30.06.2021
https://doi.org/10.51477/mejs.801367

Öz

Kaynakça

  • [1] M. C. Methods, Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning, EMAp, Fund. Getulio Vargas, Rio Janeiro, Brazil, vol. I, 2019 . [2] S. G. Ahmed, A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients, pp. 1–7, 2012.
  • [3] R. Kragler, Solution of 1d / 2d Advection-Diffusion Equation Using the Method of Inverse Differential Operators (MIDO), weingarten.de/web/kragler/mathematica October 2015.
  • [4] A. Kumar, D. K. Jaiswal, and N. Kumar, Analytical solutions of one-dimensional advection – diffusion equation with variable coefficients in no. 5, pp. 539–549, 2009.
  • [5] N. M. Abbasi, Analytical solution to diffusion-convection PDE in 1D, no. 2, pp. 1–7, 2019.
  • [6] D. K. Jaiswal, A. Kumar, and R. R. Yadav, Analytical Solution to the One-Dimensional Advection Diffusion Equation with Temporally Dependent Coefficients, vol. 2011, no. January, pp. 76–84, 2011.
  • [7] J. Biazar and H. Ghazvini, Homotopy perturbation method for solving hyperbolic partial differential equations, Comput. Math. with Appl., vol. 56, no. 2, pp. 453–458, 2008.
  • [8] M. Dehghan, On the Numerical Solution of the One-Dimensional Convection-Diffusion Equation, Vol. 2, No. July 2004, Pp. 61–74, 2005.
  • [9] M. Yaseen and M. Samraiz, The Modified New Iterative Method for Solving Linear and Nonlinear Klein Gordon Equations New Iterative Method [2],” vol. 6, no. 60, pp. 2979–2987, 2012.
  • [10] R. Behl, A. Cordero, and J. R. Torregrosa, New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns, pp. 1–17, 2018.
  • [11] A. Mathematics, S. Bhalekar, and V. Gejji, “New Iterative Method : Application to Partial Differential Equations,” no. September 2008, 2019.
  • [12] C. Chun, “A new iterative method for solving nonlinear equations,” vol. 178, pp. 415–422, 2006.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Fizik
Bölüm Makale
Yazarlar

Falade Kazeem Iyanda 0000-0001-7572-5688

Muhammad Mustapha Bu kişi benim

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 28 Eylül 2020
Kabul Tarihi 11 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 7 Sayı: 1

Kaynak Göster

IEEE F. Kazeem Iyanda ve M. Mustapha, “APPLICATION OF NEW ITERATIVE ALGORITHM FOR SOLVING NONLINEAR CONVECTION-DIFFUSION HEAT EQUATION WITH CONSTANT COEFFICIENTS”, MEJS, c. 7, sy. 1, ss. 11–23, 2021, doi: 10.51477/mejs.801367.

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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