Numerical solution of a boundary value problem including both delay and boundary layer

Abstract

Difference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is analyzed. Also, the method is proved that it gives essentially first order parameter-uniform convergence in the discrete maximum norm. Furthermore, numerical results are presented in support of the theory.

Keywords

• singular perturbation
• boundary-value problem
• finite difference method
• delay differential equation
• Shishkin mesh