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Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid

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Abstract

A singularly perturbed two-point boundary value problem with an exponential boundary layer is solved numerically by using an adaptive grid method. The mesh is constructed adaptively by equidistributing a monitor function based on the arc-length of the approximated solutions. A first-order rate of convergence, independent of the perturbation parameter, is established by using the theory of the discrete Green's function. Unlike some previous analysis for the fully discretized approach, the present problem does not require the conservative form of the underlying boundary value problem.

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Authors and Affiliations

  1. Department of Mathematics, Xiangtan University, Hunan, People's Republic of China

    Yanping Chen

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  1. Yanping Chen
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Correspondence to Yanping Chen.

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Dedicated to Dr. Charles A. Micchelli for his 60th birthday

Mathematics subject classifications (2000)

65L10, 65L12.

This work is supported by National Science Foundation of China, the key project of China State Education Ministry and Hunan Education Commission.

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Chen, Y. Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid. Adv Comput Math 24, 197–212 (2006). https://doi.org/10.1007/s10444-004-7641-0

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  • DOI: https://doi.org/10.1007/s10444-004-7641-0

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