Solving a partially singularly perturbed initial value problem on Shishkin meshes (Q846408)

The authors analyse a new numerical method for the solution of partially singularly perturbed systems of two coupled ordinary differential equations. Partially singularly perturbed is understood in the sense that one of the coupled equations is singularly perturbed while the other is not. A Shishkin-type piecewise uniform mesh is constructed in conjunction with a classical finite difference scheme resulting in a new method. It is proved that convergence of the new method is essentially of the first order in the max norm uniformly with respect to the perturbation parameter. Numerical results are given.