A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

Ishwariya Raj, Princy Mercy Johnson, John J.H Miller, Valarmathi Sigamani

Abstract


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.


Keywords


Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.

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DOI: http://dx.doi.org/10.11145/j.biomath.2016.08.111

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ISSN 1314-7218 (online)
ISSN 1314-684X (print)

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