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Bakhvalov, N.S. (1969) On Optimization of Methods for Solving Boundary-Value Problems in the Presence of a Boundary Layer. The Use of Special Transformations in the Numerical Solution of Bounary-Layer Problems. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 9, 841-859.

has been cited by the following article:

• TITLE: A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

  AUTHORS: Musa Çakır, Derya Arslan

  KEYWORDS: Singular Perturbation, Fitted Finite Difference Method, Shishkin Mesh, Nonlocal Boundary Condition, Uniform Convergence

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.6, June 29, 2016

  ABSTRACT: We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.