Difference solution and parameter estimation of one dimensional convection-diffusion equation
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Author(s)
Abstract
The Crank-Nicolson and upwind difference schemes are used to solve the one dimensional convection-diffusion equation. Then the numerical solutions obtained and the exact solution are implemented to estimate the parameters, i.e. the convection and diffusion coefficients in this type equation by the least squares method. The simulation results demonstrate that the estimation error by using Crank-Nicolson numerical solution is smaller than that by the upwind difference format. This conclusion tells us that the good accuracy of numerical solution can improve the validity of the estimation parameters in the convection-diffusion equation.
Keywords
Convection-diffusion equation; Crank-Nicolson difference scheme; upwind difference method; parameter estimation.
Cite this paper
Xiaoyang Zheng, Yuling Zeng, Qiulin Huang, Chengyou Luo, Wei wang,
Difference solution and parameter estimation of one dimensional convection-diffusion equation
, SCIREA Journal of Mathematics.
Volume 4, Issue 2, April 2019 | PP. 26-36.
References
[ 1 ] | A. Mohammadi, M. Manteghian and A. Mohammadi, Numerical solution of the one-dimensional advection-diffusion equation using simultaneously temporal and spatial weighted parameters. Australian Journal of Basic and Applied Sciences, 5 (2011), 1536-1543. |
[ 2 ] | Australian Journal of Basic and Applied Science ,5(2011),1536-1543. |
[ 3 ] | J. D. Murray, Mathematical Biology: I. An Introduction, Interdisciplinary Applied Mathematics. Springer, New York, NY, USA, 3rd edition,17 (2002). |
[ 4 ] | M.Y Kima, M.F. Wheelerb, A multiscale discontinuous Galerkin method for convection–diffusion–reaction problems. Computers and Mathematics with Applications, 68(2014), 2251-2261. |
[ 5 ] | G.D. Thiart, Finite difference scheme for the numerical solution of fluid flow and heat transfer problems on nonstaggered grids. Numerical Heat Transfer, 17(1990), 43-62. |
[ 6 ] | J. Bear, Dynamics of Fluid in Porous Media. Elsevier, New York, 1970. |
[ 7 ] | M.T.van Genuchten and W.J.Alves, Analytical solutions of the one-dimensional convective-dispersive solute transport equation. USDA Tech. Bull. 1661,1982. |
[ 8 ] | M. Dehghan, Weighted finite difference techniques for one dimensional advection-difffusion equation. Appl.Math.Comput., 147(2004), 307-319. |
[ 9 ] | J. Isenberg and C. Gutfinger, Heat transfer to a draining film. International Journal of Heat and Mass Transfer, 16 (1973), 505–511. |
[ 10 ] | Yan Ping, Yang Qing et al. Crank-Nicolson characteristic compact difference scheme for one-dimensional convection-diffusion equation. Journal of Shandong Normal University, 2017(2). |
[ 11 ] | F. Badrot-Nico, F. Brissaud, V. Guinot, A finite volume upwind scheme for the solution of the linear advection-diffusion equation with sharp gradients in multiple dimensions. Advances in Water Resources, 30 (2007) 2002-2025. |
[ 12 ] | M. Dehghan, Weighted finite difference techniques for one dimensional advection-difffusion equation. Appl.Math.Comput., 147(2004), 307-319. |
[ 13 ] | J. Isenberg and C. Gutfinger, Heat transfer to a draining film. International Journal of Heat and Mass Transfer, 16 (1973), 505–511. |
[ 14 ] | D. Liang and W. Zhao, A high-order upwind method for the convection-diffusion problem. Comput. Methods Appl. Mech. Engrg. 147 (1997), 105–115. |
[ 15 ] | M. Dehghan, On the numerical solution of the one dimensional convection-diffusion equation. Mathematical Problems in Engineering, 1(2005), 61–73. |
[ 16 ] | A. Golbabai and M. Javidi, A spectral domain decomposition approach for the generalized Burger’s-Fisher equation, Chaos, Solitons & Fractals, 1(2009), 385–392. |
[ 17 ] | A. Kumar, D. K. Jaiswal and N. Kumar, Analytical Solutions to One-Dimensional Advection-Diffusion Equa-tion with Variable Coefficients in Semi-Infinite Media, Journal of Hydrology, 380 (2010), 330-337. |
[ 18 ] | Xiaoyang Zheng, Zhengyuan Wei,Discontinuous Legendre Wavelet Galerkin Method for One-Dimensional Advection-Diffusion Equation,Applied Mathematics, 6(2015), 1581-1591. |