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

Mustafa GÜLSU, Yalçn ÖZTÜRK
DOI: 10.4236/ajcm.2011.14024                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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