Discrete Spline Solution of Singularly Perturbed Problem with Two Small Parameters on a Shishkin-Type Mesh

We consider singularly perturbed problems of convection-diffusion-reaction type which involve two small parameters. A new discrete cubic spline method is developed for the solution of this problem on a Shishkin mesh. A convergence analysis is given and the method is shown to be almost second-order uniformly convergent with respect to the perturbation parameters 𝜀d and 𝜀c. Numerical results are presented to validate the theoretical results as well as the robustness of the method.