Fitted operator method for parabolic singularly perturbed convection-diffusion problems via polynomial cubic spline

This article introduces a new fitted operator method for singularly perturbed parabolic convection-diffusion having right boundary layer. We approximate the time derivative using the implicit Euler’s approach and the spatial derivative using polynomial cubic spline method. Using the idea of a singular perturbation, a fitting factor is added to the scheme. The resulting tridiagonal system of equations is solved using Thomas algorithm. We demonstrate the order of convergence and the proposed method have order two in space variable and order one in time variable. Three numerical examples are considered to illustrate the applicability of the present methods and compared with the methods produced by different authors. In general, the presented method is \(\epsilon \) $ϵ$ -uniformly convergent for any values of mesh size and more accurate than some methods existing in the literature.