Dissipative particle dynamics (DPD) is a mesoscopic simulation method that describes "clusters" of molecules as a single numerical particle. DPD is a very effective method but it introduces numerical artifacts through the coarse-graining procedure, such as particle ordering in the near-wall region. These artifacts can result in nonphysical phenomena during a simulation of a polymer tethered to the wall undergoing shear flow: polymer sticking and overextension for higher shear rates. In this paper we report that a version of DPD with a so-called solidification boundary formulation and conservative-force interactions based on the equation of state allows to reduce number density fluctuations in near-wall region significantly.