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Kopteva, N.V. (1997) On the Uniform in Small Parameter Convergence of a Weighted Scheme for the One-Dimensional Time-Dependent Convection-Diffusion Equation. Computational Mathematics and Mathematical Physics, 37, 1173-1180.

has been cited by the following article:

• TITLE: Numerical Solution of Quasilinear Singularly Perturbed Problems by the Principle of Equidistribution

  AUTHORS: Quan Zheng, Fulin Ye

  KEYWORDS: Quasilinear Singularly Perturbed BVP, Equidistribution, Adaptive Mesh, Uniform Convergence

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.10, October 23, 2020

  ABSTRACT: In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed.