Mathematics Research Institute

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"A uniformly convergent method to solve 1D parabolic singularly perturbed reaction-diffusion problems"

Carmelo Clavero (Universidad de Zaragoza)

Fecha: 10/07/2013 11:00
Lugar: Sala de Grados I de la Facultad de Ciencias.
Grupo: GIR Análisis Numérico de Problemas de Evolución

In this talk we are interested in approximating the solution of one dimensional parabolic singularly perturbed problems of reaction-diffusion type. We construct a numerical method combining the Crank-Nicolson method on a uniform mesh, to discretize in time, and the classical central finite difference scheme, on a special nonuniform mesh condensing the grid points in the boundary layer regions, to discretize in space. We prove that the fully discrete scheme is a second order parameter uniform convergent method in the maximum norm. The proof of the convergence is based on splitting the contribution to the global error of both the time and the spatial discretizations. We show the results obtained for different test problems, illustrating in practice the order of uniform convergence of the numerical method.