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Uniform convergence analysis of finite difference approximations for general singular perturbed problem on adaptive grids

Volume 7, Issue 2, April 2022    |    PP. 57-67    |PDF (281 K)|    Pub. Date: May 8, 2022
DOI: 10.54647/physics14429    10 Downloads     132 Views  

Author(s)
Linan Sun, College of Resources and Environment, Henan University of Economics and Law, Zhengzhou 450046, China; College of Geography and Environmental Science, Henan University, Kaifeng 475004, China
Antao Wang, Department of cyber security, Henan Police College, Zhengzhou 450046, China

Abstract
In this paper we consider a more general singular perturbation problem, that is, -epsilon u ''(x) - a(x)u'(x) + b(x)u(x) = f(x) (0 < epsilon << 1) on an adaptive grid. The mesh is constructed adaptively by equidistributing a monitor function based on the arc-length of the approximated solutions. Our analysis provide insight into the convergence behaviour on such mesh, and the posterior error estimates of piecewise linear interpolation about the approximate solution is investigated and an epsilon-uniform error estimate for the first-order upwind discretization of general singular perturbed problem is derived at last. We extend the relevant results of the document to a more general case.

Keywords
adaptive grids; general singular perturbed problem; convergence analysis; posterior error estimates

Cite this paper
Linan Sun, Antao Wang, Uniform convergence analysis of finite difference approximations for general singular perturbed problem on adaptive grids, SCIREA Journal of Physics. Vol. 7 , No. 2 , 2022 , pp. 57 - 67 . https://doi.org/10.54647/physics14429

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