numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  into two subintervals called inner region (boundary layer region) and outer region. the shooting method  is applied to inner region whereas for the outer region, standard finite difference method is applied.  necessary error estimates are derived. computational efficiency and accuracy are verified through numerical examples.