Open AccessA parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
Author(s) -
Ishwariya Raj,
Princy Mercy Johnson,
John J. H. Miller,
Valarmathi Sigamani
Publication year - 2016
Publication title -
biomath
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.252
H-Index - 3
eISSN - 1314-7218
pISSN - 1314-684X
DOI - 10.11145/i.biomath.2016.08.111
Subject(s) - mathematics , mathematical analysis , singular perturbation , piecewise , uniform convergence , differential equation , piecewise linear function , method of matched asymptotic expansions , perturbation (astronomy) , norm (philosophy) , initial value problem , numerical analysis , first order , physics , computer network , bandwidth (computing) , quantum mechanics , computer science , political science , law
In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.