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**A numerical method for a singularly perturbed three-point boundary value problem.**
*(English)*
Zbl 1191.65098

Summary: The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter \(\epsilon \), of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

65L12 | Finite difference and finite volume methods for ordinary differential equations |

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |

34E15 | Singular perturbations for ordinary differential equations |

### Keywords:

singular perturbation; uniform finite difference method; convection-diffusion problem; piecewise uniform Shishkin type mesh; numerical experiments; convergence
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\textit{M. Çakır} and \textit{G. M. Amiraliyev}, J. Appl. Math. 2010, Article ID 495184, 17 p. (2010; Zbl 1191.65098)

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### References:

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