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The first part of this paper is conceed with the well-posedness for the rigid rod-like model in shear flow of a polymeric fluid. The constitutive relations considered in this work are motivated by the kinetic theory. The stress tensor is given by an integral which involves the solution of the Fokker-Planck equation. A novel numerical scheme for the FokkerPlanck equation is proposed, which preserves the positivity of the distribution function.Another part of this work establishes the convergence theory of the fully discretized schemes for a simple micro-macro simulation of a polymeric flow.