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Abstract. This paper deals with constructing monotone schemes of the second-order accuracy in space for transient convection-diffusion problems. They are based on a reformulation of the convective and diffusive transport terms using the convective terms in the divergent and nondivergent forms. The stability of the difference schemes is established in the uniform and L1 norm. For 2D problems, unconditionally monotone schemes of splitting with respect to spatial variables are developed. Unconditionally stable schemes for problems of convection-diffusion-reaction are proposed, too.

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