zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A Robust computational method for singularly perturbed coupled system of reaction-diffusion boundary-value problems. (English) Zbl 1130.65082
The authors devise a robust computational method for singularly perturbed systems of reaction-diffusion boundary-value problems on a piecewise uniform Shishkin mesh on the whole domain. They prove that this newly proposed scheme is uniformly stable throughout the domain and provides second-order uniform convergence results, and give a test problem to verify the efficiency and accuracy of the method.

65L20Stability and convergence of numerical methods for ODE
65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
65L50Mesh generation and refinement (ODE)
Full Text: DOI
[1] Bawa, R. B.; Natesan, S.: Uniformly convergent computational technique for singularly perturbed self-adjoint mixed boundary-value problems. Lect. notes comput. Sci. 3516, 1104-1107 (2005) · Zbl 1120.65322
[2] Bawa, R. K.; Natesan, S.: A computational method for self-adjoint singular perturbation problems using quintic spline. Comput. math. Appl., No. 50, 1371-1382 (2005) · Zbl 1084.65070
[3] Farrell, P. A.; Hegarty, A. F.; Miller, J. J. H.; O’riordan, E.; Shishkin, G. I.: Robust computational techniques for boundary layers. (2000) · Zbl 0964.65083
[4] Kadalbajoo, M. K.; Bawa, R. K.: Variable mesh difference scheme for singularly perturbed boundary value problems using splines. J. optim. Theory appl. 9, 405-416 (1996) · Zbl 0951.65070
[5] Linß, T.; Madden, N.: Accurate solution of a system of coupled singularly perturbed reaction -- diffusion equations. Computing 73, 121-133 (2004) · Zbl 1057.65046
[6] Madden, N.; Stynes, M.: A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction -- diffusion problems. IMA J. Numer. anal. 23, 627-644 (2003) · Zbl 1048.65076
[7] Matthwes, S.; O’riordan, E.; Shishkin, G. I.: A numerical method for a system of singularly perturbed reaction -- diffusion equations. J. comput. Appl. math. 145, 151-166 (2002)
[8] Miller, J. J. H.; O’riordan, E.; Shishkin, G. I.: Fitted numerical methods for singular perturbation problems. (1996)
[9] Natesan, S.; Bawa, R. K.; Carmelo, C.: An &z.epsiv;-uniform hybrid scheme for singularly perturbed 1-d reaction -- diffusion problems. Proceedings of the sixth European conference on numerical mathematics and advanced applications (ENUMATH 2005), university of Santiago de Compostela, Spain, 1025-1032 (2006)
[10] Natesan, S.; Ramanujam, N.: Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations. Appl. math. Comput. 98, 119-137 (1999) · Zbl 0940.65080
[11] Roos, H. -G.: Layer-adapted grids for singular perturbation problems. Z. angew. Math. mech. 78, 291-309 (1998) · Zbl 0905.65095
[12] Roos, H. -G.; Stynes, M.; Tobiska, L.: Numerical methods for singularly perturbed differential equations. (1996) · Zbl 0844.65075