Difference solution and parameter estimation of one dimensional convection-diffusion equation

Volume 4, Issue 2, April 2019     |     PP. 26-36      |     PDF (1442 K)    |     Pub. Date: April 26, 2019
DOI:    378 Downloads     7426 Views  

Author(s)

Xiaoyang Zheng, Institute of Liangjiang Artificial Intelligence, Chongqing University of Technology, Chongqing, China
Yuling Zeng, College of Science, Chongqing University of Technology, Chongqing, China
Qiulin Huang, College of Science, Chongqing University of Technology, Chongqing, China
Chengyou Luo, College of Science, Chongqing University of Technology, Chongqing, China
Wei wang, Institute of Liangjiang Artificial Intelligence, Chongqing University of Technology, Chongqing, China

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.

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