APPLICATION OF NEW ITERATIVE ALGORITHM FOR SOLVING NONLINEAR CONVECTION-DIFFUSION HEAT EQUATION WITH CONSTANT COEFFICIENTS
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.
Anahtar Kelimeler
Convection-diffusion heat equation new iterative method (NIM), convection-diffusion constant coefficients
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.
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematiksel Fizik |
| Bölüm | Makale |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2021 |
| Gönderilme Tarihi | 28 Eylül 2020 |
| Kabul Tarihi | 11 Mart 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 7 Sayı: 1 |
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