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Volume 35, Issue 3
A Nearly Analytic Discrete Method for One-Dimensional Unsteady Convection-Dominated Diffusion Equations

Yon-Chol Kim, Nam Yun & Dong-Ho Chai

DOI: 10.13447/j.1674-5647.2019.03.01

Commun. Math. Res., 35 (2019), pp. 193-207.

Published online: 2019-12

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  • 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.


  • Keywords

convection-dominated diffusion equation, nearly analytic discretization method, analysis of the stability

  • AMS Subject Headings

76Rxx, 65N12, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yonchol126@163.com (Yon-Chol Kim)

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-193, author = {Kim , Yon-CholYun , Nam and Chai , Dong-Ho}, title = {A Nearly Analytic Discrete Method for One-Dimensional Unsteady Convection-Dominated Diffusion Equations}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {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.


}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.01}, url = {http://global-sci.org/intro/article_detail/cmr/13525.html} }
TY - JOUR T1 - A Nearly Analytic Discrete Method for One-Dimensional Unsteady Convection-Dominated Diffusion Equations AU - Kim , Yon-Chol AU - Yun , Nam AU - Chai , Dong-Ho JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 207 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.03.01 UR - https://global-sci.org/intro/article_detail/cmr/13525.html KW - convection-dominated diffusion equation, nearly analytic discretization method, analysis of the stability AB -

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.


Kim , Yon-CholYun , Nam and Chai , Dong-Ho. (2019). A Nearly Analytic Discrete Method for One-Dimensional Unsteady Convection-Dominated Diffusion Equations. Communications in Mathematical Research . 35 (3). 193-207. doi:10.13447/j.1674-5647.2019.03.01
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