A new numerical method for simulating the solar wind Alfvén waves: Development of the Vlasov-MHD model

► A novel scheme of plasma simulation for computing solar wind Alfvén waves is developed. ► The scheme is based on the Vlasov and the MHD models, for solving the longitudinal and the transverse components. ► The scheme can correctly describe evolution of weakly nonlinear parallel Alfvén waves in the linear and nonlinear stages.