Author(s)

Musa Çakır, Derya Arslan

Department of Mathematics, Faculty of Science, University of Yuzuncu Yil, Van, Turkey.

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.

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

Çakır, M. and Arslan, D. (2016) A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem. Journal of Applied Mathematics and Physics, 4, 1143-1156. doi: 10.4236/jamp.2016.46119.