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A Nearly Analytic Discrete Method for One-dimensional Unsteady Convection-dominated Diffusion Equations

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【作者】 KIM YON-CHOLYUN NAMCHAI DONG-HO

【Author】 KIM YON-CHOL;YUN NAM;CHAI DONG-HO;Institute of Mathematics, Academy of Sciences of DPR Korea;

【机构】 Institute of Mathematics, Academy of Sciences of DPR Korea

【摘要】 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(τ~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.

【基金】 Foundation (62120170) of the IMSAS
  • 【DOI】10.13447/j.1674-5647.2019.03.01
  • 【分类号】O35
  • 【下载频次】3
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