**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31533

##### Alternative Convergence Analysis for a Kind of Singularly Perturbed Boundary Value Problems

**Authors:**
Jiming Yang

**Abstract:**

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

**Keywords:**
Convergence analysis,
green's function,
singularly perturbed,
equi-distribution,
moving mesh.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1071520

**References:**

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[2] Y. Chen, Uniform convergence analysis of finite difference approximations for singularly perturbed problems on an adapted grid, Advances in Computational Mathematics, 24(1-4) (2006), 197-212.

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[9] J. Yang and Y. Chen, A moving mesh method for a singularly perturbed convection-diffusion boundary value problem (in Chinese), Natural science journal of xiangtan university, 26(3) (2004), 24-29.