Original scientific paper
Second order parameter--uniform convergence for a finite difference method for a singularly perturbed linear reaction--diffusion system
Paramasivam Mathiyazhagan
; Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India
Valarmathi Sigamani
; Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India
John J. H. Miller
; Institute for Numerical Computation and Analysis, Dublin, Ireland
Abstract
A singularly perturbed linear system of second order ordinary
differential equations of reaction-diffusion type with given
boundary conditions is considered. The leading term of each equation
is multiplied by a small positive parameter. These singular
perturbation parameters are assumed to be distinct. The components
of the solution exhibit overlapping layers. Shishkin
piecewise--uniform meshes are introduced, which are used in
conjunction with a classical finite difference discretisation, to
construct a numerical method for solving this problem. It is proved
that the numerical approximations obtained with this method are
essentially second order convergent uniformly with respect to all of
the parameters.
Keywords
Singular perturbation problems; system of differential equations; reaction--diffusion; overlapping boundary layers; classical finite difference scheme; Shishkin mesh; parameter--uniform convergence
Hrčak ID:
61881
URI
Publication date:
8.12.2010.
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