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Volume 7, Issue 3
A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I

M. Viscor & M. Stynes

Int. J. Numer. Anal. Mod., 7 (2010), pp. 549-566.

Published online: 2010-07

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  • 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.

  • Keywords

Singularly perturbed, degenerate parabolic problem, Shishkin mesh.

  • AMS Subject Headings

65M06, 65M12, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-549, author = {M. Viscor and M. Stynes}, title = {A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/737.html} }
TY - JOUR T1 - A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I AU - M. Viscor & M. Stynes JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 549 EP - 566 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/737.html KW - Singularly perturbed, degenerate parabolic problem, Shishkin mesh. AB -

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.

M. Viscor and M. Stynes. (2010). A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I. International Journal of Numerical Analysis and Modeling. 7 (3). 549-566. doi:
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