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This study deals with a new approach method for solving singularly perturbed boundary value problem of convection-diffusion type. Firstly, bounds on the solution and its derivative of solution to be used later in the article are obtained. This robust method is constructed with fitted difference scheme on a uniform mesh. It is proved that the presented method is first-order convergent with respect to the perturbation parameter e in the discrete maximum norm. Two examples are given to illustrate the efficiency of the method. The numerical results are presented in tables and figures.

A Novel Numerical Approach for Solving Convection-Diffusion Problem with Boundary Layer Behavior