Richardson extrapolation on generalized Shishkin meshes for singularly perturbed problems

• Autores: José Luis Gracia Lozano, Carmelo Clavero Gracia
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 169-178
• Idioma: inglés
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• Resumen

  • In this work we are interested in to apply the Richardson extrapolation technique on a type of finite difference schemes, which are used to solve 1D singularly perturbed problems of convection-diffusion type. The numerical method is constructed on generalized Shishkin meshes, which are defined by using a generating function; in all cases the mesh points are condensed in the boundary layer region, in order to obtain a good approximation in the maximum norm. We prove that, if the diffusion coefficient is sufficiently small, an appropriate Richardson extrapolation increase the order of uniform convergence associated to the basic finite difference scheme. Some numerical examples permit us to confirm in practice the theoretical results.