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Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems
Author(s):
E.
O'Riordan;
M.
L.
Pickett;
G.
I.
Shishkin.
Journal:
Math. Comp.
75
(2006),
1135-1154.
MSC (2000):
Primary 65M06, 65M15;
Secondary 65M12
Posted:
April 3, 2006
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Abstract:
In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
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Additional Information:
E.
O'Riordan
Affiliation:
School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email:
eugene.oriordan@dcu.ie
M.
L.
Pickett
Affiliation:
School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email:
maria.pickett2@mail.dcu.ie
G.
I.
Shishkin
Affiliation:
Institute for Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
Email:
shishkin@imm.uran.ru
DOI:
10.1090/S0025-5718-06-01846-1
PII:
S 0025-5718(06)01846-1
Keywords:
Two parameter,
reaction-convection-diffusion,
piecewise-uniform mesh
Received by editor(s):
September 22, 2004
Posted:
April 3, 2006
Additional Notes:
This research was supported in part by the National Center for Plasma Science and Technology Ireland, by the Enterprise Ireland research scholarship BR-2001-110 and by the Russian Foundation for Basic Research under grant No. 04-01-00578.
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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