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.