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• W173935863 abstract "In this work we prove the uniform convergence of high order of some numerical methods used to solve a type of linear reaction-diffusion singularly perturbed problems. Firstly, we will consider the case of 1D stationary problems; based on the central finite difference scheme, constructed on a piecewise uniform Shishkin mesh, a new method of HODIE type is defined having third order of e-uniform convergence in the maximum norm. Using this HODIE scheme jointly with a two stage SDIRK method, we solve a 1D parabolic singularly perturbed problem. Finally, we consider a parabolic 2D problem of the same type; in this case, the HODIE scheme is combined with a fractional step Runge Kutta method. In both time dependent problems, the resulting methods have third order of uniform convergence with respect both time and spatial variables. We show some numerical experiments confirming the theoretical results. 2000 Mathematics Subject Classification: 65N12; 65N30; 65N06." @default.
• W173935863 created "2016-06-24" @default.
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• W173935863 date "2003-01-01" @default.
• W173935863 modified "2023-09-24" @default.
• W173935863 title "Some methods of order three for reaction-diffusion problems" @default.
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