A numerical method for a singularly perturbed three-point boundary value problem.
Çakır, Musa, Amiraliyev, Gabil M. (2010)
Journal of Applied Mathematics
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Çakır, Musa, Amiraliyev, Gabil M. (2010)
Journal of Applied Mathematics
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In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference...
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The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
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Advances in Difference Equations [electronic only]
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