A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I

A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I

Year:    2010

International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 549–566

Abstract

A singularly perturbed degenerate parabolic problem in one space dimension is considered. Bounds on derivatives of the solution are proved; these bounds depend on the two data parameters that determine how singularly perturbed and how degenerate the problem is. A tensor product mesh is constructed that is equidistant in time and of Shishkin type in space. A finite difference method on this mesh is proved to converge; the rate of convergence obtained depends on the degeneracy parameter but is independent of the singular perturbation parameter. Numerical results are presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2010-IJNAM-737

International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 549–566

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Singularly perturbed degenerate parabolic problem Shishkin mesh.