Exponentially fitted cubic spline for two-parameter singularly perturbed boundary value problems

In this paper, we derive an exponentially fitted difference scheme using cubic splines for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The solution of the problem exhibits a boundary layer on the left-hand side of the domain. Bounds on the derivatives of the solution are derived. A first-order numerical method is constructed. Numerical results are presented to establish the theoretical results and to show the efficiency of the method.