Computational treatment of a convection-diffusion type nonlinear system of singularly perturbed differential equations

In this article, a nonlinear system of singularly perturbed differential equations of convection-diffusion type with Dirichlet boundary conditions is considered on the interval [۰,۱]. Both components of the solution of the system exhibit boundary layers near t = ۰. A new computational method involving classical finite difference operators, a piecewise-uniform Shishkin mesh and an algorithm based on the continuation method is developed to compute the numerical approximations. The computational method is proved to be first order convergent uniformly with respect to the perturbation parameters.  Numerical experiments  support the theoretical results.

Keywords:

Nonlinear system of singularly perturbed differential equations , boundary layers , finite difference scheme , Shishkin mesh , the continuation method , parameter-uniform convergence