TY - JOUR
T1 - A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I
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 - <p style="text-align: justify;">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.</p>