Fourth-order finite-difference method for boundary value problems with two small parameters

We present a finite difference scheme for a class of linear singularly perturbed boundary value problems with two small parameters. The problem is discretized using a Bakhvalov-type mesh. It is proved under certain conditions that this scheme is fourth-order accurate and that its error does not increase when the perturbation parameter tends to zero. Numerical examples are presented which demonstrate computationally the fourth order of the method.