  The main purpose of this paper is to present a new corrected decoupled scheme
combined with a spatial finite volume method for chemotaxis models. First, we
derive the scheme for a parabolic-elliptic chemotaxis model arising in
embryology. We then establish the existence and uniqueness of the numerical
solution, and we prove that it converges to a corresponding weak solution for
the studied model. In the last section, several numerical tests are presented
by applying our approach to a number of chemotaxis systems. The obtained
numerical results demonstrate the efficiency of the proposed scheme and its
effectiveness to capture different forms of spatial patterns.
