High‐order numerical methods for one‐dimensional parabolic singularly perturbed problems with regular layers

In this work we construct and analyse some finite difference schemes used to solve a class of time-dependent one-dimensional convection-diffusion problems, which present only regular layers intheir solution. We use the implicit Euler or the Crank-Nicolson method to discretize the timevariable and a HODIE finite difference scheme, defined on a piecewise uniform Shishkin mesh,to discretize the spatial variable. In both cases we prove that the numerical method is uniformlyconvergent with respect to the diffusion parameter, having order near two in space and order oneor 3

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