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Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid
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American Journal of Computational Mathematics·Volume 01 (2011)·Pages 209–218·Published 22 December 2011·DOI10.4236/ajcm.2011.14024
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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.
KeywordsSingular Perturbation ProblemsTwo-Point Boundary Value ProblemsThe Shifted Chebyshev PolynomialsApproximation MethodMatrix Method
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