A Nearly Analytic Discrete Method for One-Dimensional Unsteady Convection-Dominated Diffusion Equations
Year: 2019
Author: Yon-Chol Kim, Nam Yun, Dong-Ho Chai
Communications in Mathematical Research , Vol. 35 (2019), Iss. 3 : pp. 193–207
Abstract
In this paper, a nearly analytic discretization method for one-dimensional linear unsteady convection-dominated diffusion equations and viscous Burgers' equation as one of the nonlinear equation is considered. In the case of linear equations, we find the local truncation error of the scheme is $O(\tau^2+h^4)$ and consider the stability analysis of the method on the basis of the classical von Neumann's theory. In addition, the nearly analytic discretization method for the one-dimensional viscous Burgers' equation is also constructed. The numerical experiments are performed for several benchmark problems presented in some literatures to illustrate the theoretical results. Theoretical and numerical results show that our method is to be higher accurate and nonoscillatory and might be helpful particularly in computations for the unsteady convection-dominated diffusion problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2019.03.01
Communications in Mathematical Research , Vol. 35 (2019), Iss. 3 : pp. 193–207
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: convection-dominated diffusion equation nearly analytic discretization method analysis of the stability