DOI: 10.1002/num.20030

# High Order Numerical Methods For One Dimensional Parabolic Singularly Perturbed Problems With Regular Layers

Carmelo Clavero Gracia, Juan Carlos Jorge Ulecia, José Luis Gracia Lozano

Published 2003 · Mathematics

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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