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

• Main Authors: Ishwariya Raj, Princy Mercy Johnson, John J.H Miller, Valarmathi Sigamani
• Format: Article
• Language: English
• Published: Biomath Forum 2016-09-01
• Series: Biomath
• Subjects: Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.
• Online Access: http://www.biomathforum.org/biomath/index.php/biomath/article/view/573
• ISSN: 1314-684X; 1314-7218

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.