@inproceedings{65ac4fad1bb1470c95006d852a8d796c,

title = "Parameter-uniform numerical methods for a class of singularly perturbed problems with a neumann boundary condition",

abstract = "The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed modelo rdinary differentiale quations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. For the same classicalfini te difference operator on an appropriate piecewise–uniform mesh, it is shown that the numerical solutions converge, uniformly with respect to the perturbation parameter, to the exact solution of any problem from this class.",

author = "Farrell, {P. A.} and Hegarty, {A. F.} and Miller, {J. J.} and E. O{\textquoteright}Riordan and Shishkin, {G. I.}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2001.; 2nd International Conference on Numerical Analysis and Its Applications, NAA 2000 ; Conference date: 11-06-2000 Through 15-06-2000",

year = "2001",

doi = "10.1007/3-540-45262-1_35",

language = "English",

isbn = "9783540418146",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "292--303",

editor = "Lubin Vulkov and Plamen Yalamov and Jerzy Waniewski",

booktitle = "Numerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers",

}