Measured growth rates as a function of resolution for the linA mode of the streaming instability from Youdin & Johansen (2007). This mode is for particles of dimensionless stopping time ﹩{\tau }_{s}=0.1﹩ and a background solid-to-gas density ratio of ﹩{\epsilon }_{0}=3﹩. The resolution is expressed in number of cells per wavelength λ of the mode, where Δ is the cell size. The rates s are expressed in terms of the local angular speed Ω and are measured over the time interval ﹩0\leqslant t\leqslant 0.2P﹩, where ﹩P=2\pi /{\rm{\Omega }}﹩ is the local orbital period. The top row shows the three components of the particle velocity field ﹩{\boldsymbol{v}}﹩ and the particle density field ﹩{\rho }_{p}﹩, while the bottom row shows the three components of the gas velocity field ﹩{\boldsymbol{u}}﹩ and the gas density field ﹩{\rho }_{g}﹩. The solid lines denote the theoretical growth rate. The blue circles are the results obtained with the original explicit integration, while the red diamonds and the green squares are the results computed by our algorithm with and without the particle-mesh treatment of the back reaction, respectively, which is described in Section 2.3.