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

Authors

  • Ishwariya Raj Bishop Heber College, Tiruchirappalli-620017 Tamil Nadu, India
  • Princy Mercy Johnson Bishop Heber College, Tiruchirappalli-620017 Tamil Nadu, India
  • John J.H Miller Institute for Numerical Computation and Analysis, Dublin
  • Valarmathi Sigamani Bishop Heber College, Tiruchirappalli-620017 Tamil Nadu, India

DOI:

https://doi.org/10.11145/j.biomath.2016.08.111

Keywords:

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

Abstract

In this paper an initial value problem for aВ non-linear system of two singularly perturbed first orderВ differential equations is considered on the interval (0,1].
The components of the solution of this system exhibit initialВ layers at 0. A numerical method composed of a classicalВ finite difference scheme on a piecewise uniform ShishkinВ mesh is suggested. This method is proved to be almost firstВ order convergent in the maximum norm uniformly in theВ perturbation parameters.

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Published

2016-09-11

Issue

Vol. 5 No. 2 (2016)

Section

Original Articles

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