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Çakır, Musa; Amiraliyev, Gabil M.

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

J. Appl. Math. 2010, Article ID 495184, 17 p. (2010).
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.

Cited in 2 Documents

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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