Solution of convection-diffusion problems using fourth order adaptive cubic spline method

In this paper, using adaptive cubic spline, we have suggested a numerical scheme for solving a convection-diffusion problem having layer structure. The numerical scheme is derived with this spline and non-standard finite differences of the first derivative. The tridiagonal solver is used to solve the system of the numerical method. The analysis of convergence of the method is briefly discussed and the fourth order is shown. The numerical results of the examples were tabulated and compared to the existing computational results in order to support the higher accuracy of the proposed numerical scheme.