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perturbed two-point boundary value problem. – Applied Mathematics and Computation, vol.155, pp.95-110. [17] Mishra H.K., Kumar M. and Singh P. (2009): Initial value technique for self adjoint singular perturbation boundary value problems . – Computational Mathematics and modeling, vol.29, No.2. [18] Natesan S. and Ramanujam N. (1998): Initial-value technique for singularly perturbed boundary value problems for second-order ordinary differential equations arising in chemical reactor theory . – Journal of Optimization Theory and Applications, vol.97, No.2, pp.455-470. [19

Abstract

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.