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J. J. H. Miller, E. O’Riordan and G. I. Shishkin, “On Piecewise Uniform Meshes for Upwind and Central Difference Operators for Solving Singularly Perturbed Problems,” IMA Journal of Numerical Analysis, Vol. 15, No. 1, 1995, pp. 89-99. doi:10.1093/imanum/15.1.89

has been cited by the following article:

• TITLE: Spline in Compression Methods for Singularly Perturbed 1D Parabolic Equations with Singular Coefficients

  AUTHORS: Ranjan K. Mohanty, Vijay Dahiya, Noopur Khosla

  KEYWORDS: Spline in Compressions; Parabolic Equations; Two-Level Implicit Schemes; Singular Perturbation; Singular Coefficients; RMS Errors

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.2 No.2, April 27, 2012

  ABSTRACT: In this article, we discuss three difference schemes; for the numerical solution of singularity perturbed 1-D parabolic equations with singular coefficients using spline in compression. The proposed methods are of accurate and applicable to problems in both cases singular and non-singular. Stability theory of a proposed method has been discussed and numerical examples have been given in support of the theoretical results.