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M. K. Kadalbajoo and V. P. Ramesh, “Numerical Meth- ods on Shishkin Mesh for Singularly Perturbed Delay Differential Equations with a Grid Adaptation Strategy,” Applied Mathematics and Computation, Vol. 188, No. 2, 2007, pp. 1816-1831. doi:10.1016/j.amc.2006.11.046

has been cited by the following article:

• TITLE: Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid

  AUTHORS: Mustafa GÜLSU, Yalçn ÖZTÜRK

  KEYWORDS: Singular Perturbation Problems, Two-Point Boundary Value Problems, The Shifted Chebyshev Polynomials, Approximation Method, Matrix Method

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.4, December 9, 2011

  ABSTRACT: Matrix methods, now-a-days, are playing an important role in solving the real life problems governed by ODEs and/or by PDEs. Many differential models of sciences and engineers for which the existing methodologies do not give reliable results, these methods are solving them competitively. In this work, a matrix methods is presented for approximate solution of the second-order singularly-perturbed delay differential equations. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The error analysis and convergence for the proposed method is introduced. Finally some experiments and their numerical solutions are given.