**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31103

##### The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem

**Authors:**
Jiming Yang

**Abstract:**

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

**Keywords:**
singularly perturbed,
upwind difference,
uniform convergence

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1074307

**References:**

[1] R. B. Kellogg and A. Tsan., Analysis of some difference approximations for a singular perturbation problem without turning points, Math. Comp., 32(1978) 1025-1039.

[2] Y. Chen, Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution, J. Comp. Appl. Math., 159 (2003) 25-34.

[3] Y. Chen, Uniform convergence analysis of finite difference approximations for singularly perturbed problems on an adapted grid, Advances in Comp. Math., 24 (2006) 197-212.

[4] N. Kopteva and M. Stynes, A robust adaptive method for a quasi-linear one dimensional convection-diffusion problem, SIAM J. Numer. Anal., 39(2001) 1446-1467.

[5] T. Linss, Uniforming pointwise convergence of finite difference schemes using grid equidistribution, Computing, 66(2001) 27-39.

[6] Y. Qiu and D. M. Sloan, Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid, J. Comp. Appl. Math., 101(1999) 1-25.

[7] Y. Qiu, D. M. Sloan and T. Tang, Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence, J. Comp. Appl. Math., 116(2000) 121-143.

[8] V. B. Andreev and I. A. Savin, On the convergence, uniform with respect to the small parameter of A. A. Samarskii-s monotone scheme and its modifications, Comp. Math. Math. Phys., 35(1995) 581-591.

[9] V. B. Andreev and N. Kopteva, On the convergence, uniform with respect to a small parameter of monotone three-point difference approximation, Differ. Uravn., 34(1998) 921-929.