A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction – diffusion problems

@inproceedings{Madden2002AUC,
  title={A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction – diffusion problems},
  author={Niall Madden},
  year={2002}
}
A coupled system of two singularly perturbed linear reaction–diffusion two-point boundary value problems is examined. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analysed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh central… CONTINUE READING
Highly Influential
This paper has highly influenced 11 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 43 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 14 references

Numerical reaction–diffusion equations

S. MATTHEWS, E. O’RIORDAN, G. I. SHISHKIN
J . Comp . Appl . Math . • 2002
View 1 Excerpt
Highly Influenced

Parameter robust numerical methods for a system of two coupled singularly perturbed reaction–diffusion equations

S. MATTHEWS
2000
View 3 Excerpts
Highly Influenced

Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations

G. I. SHISHKIN
1995
View 2 Excerpts
Highly Influenced

A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction–diffusion problem

E. O’RIORDAN, M. STYNES
Math . Comput . • 1986
View 1 Excerpt
Highly Influenced

The necessity of Shishkin decompositions

T. L INSS
Appl . Math . Lett . • 2001

Robust computational techniques for boundary layers Vol. 16 of Applied Mathematics and Mathematical Computation

P. A. FARRELL, A. F. HEGARTY, +3 authors G. I. SHISHKIN
2000
View 1 Excerpt

Towards an improved turbulence model for wave-current interactions

G. P. THOMAS
1998
View 1 Excerpt

Fitted Numerical Methods For Singular Perturbation Problems—Error Estimates In The Maximum Norm For Linear Problems

J.J.H. MILLER, E. O’RIORDAN, G. I. SHISHKIN
In One And Two Dimensions. Singapore: World Scientific • 1996
View 1 Excerpt

Similar Papers

Loading similar papers…