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.