High-order time-accuracy schemes for parabolic singular perturbation problems with convection
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P.W. Hemker
Abstract
- The first boundary value problem for a singularly perturbed parabolic PDE with convection is considered on an interval. For the case of sufficiently smooth data, it is easy to construct a standard finite difference operator and a piecewise uniform mesh condensing in the boundary layer, which gives an e-uniformly convergent difference scheme. The order of convergence for such a scheme is exactly one and close to one up to a small logarithmic factor with respect to the time and space variables, respectively. In this paper we construct high-order time-accurate e-uniformly convergent schemes by a defect-correction technique. The efficiency of the new defect-correction scheme is confirmed by numerical experiments.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Contents
- High-order time-accuracy schemes for parabolic singular perturbation problems with convection
- On high-order compact schemes in the finite element method
- On implicit extrapolation methods for ordinary differential equations
- On error analysis in data assimilation problems
- Mathematical modelling of the three-dimensional boundary value problem of the discharge of the well system in a homogeneous layer
- Parallel realization of statistical simulation and random number generators
Articles in the same Issue
- Contents
- High-order time-accuracy schemes for parabolic singular perturbation problems with convection
- On high-order compact schemes in the finite element method
- On implicit extrapolation methods for ordinary differential equations
- On error analysis in data assimilation problems
- Mathematical modelling of the three-dimensional boundary value problem of the discharge of the well system in a homogeneous layer
- Parallel realization of statistical simulation and random number generators
