Advances in Computational Mathematics

, Volume 24, Issue 1–4, pp 197–212 | Cite as

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

  • Yanping Chen


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.


singular perturbation moving mesh rate of convergence error estimate 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsXiangtan UniversityHunanPeople's Republic of China

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