An efficient mixed asymptotic-numerical scheme for singularly perturbed convection diffusion problems

In this paper, we present and analyze a mixed asymptotic-numerical method for the solution of singularly perturbed convection diffusion problems. The technique, used in this work, is the careful factorization of original problem into two explicit problems which are independent of perturbation parameter contaminating the solution. The first problem, so obtained, is the degenerate equation which corresponds to the outer solution while the second problem is obtained by making use of suitable stretching transformation and it corresponds to the inner solution. The degenerate equation is solved numerically using q-stage Runge-Kutta method. The second problem, which retains the order of the original problem, is solved analytically. Possible extensions of the present technique to differential equations with delay as well as advance and to the nonlinear problems are also discussed. A comparative study of the present method with some state of art existing numerical schemes is carried out by means of several linear and nonlinear test examples that demonstrates the effectiveness and the potential of the present approach.