This paper develops a numerical method and applies it to the study of corotating high-speed streams in the equatorial plane of the heliosphere from 0.3 AU up to 10 AU, where corotating shocks undergo processes of formation, development, and interaction. The numerical method is designed specially for solving two-dimensional steady supersonic magnetohydrodynamic flows, and it has two distinguishing features: (1) The conservation laws are maintained with high precision along the streamlines, and (2) a shock or a tangential discontinuity is treated as a surface with zero thickness, using the Rankine-Hugoniot relations to directly match the flow conditions upstream and downstream. By using this method, the whole physical picture of the corotating high-speed streams is constructed throughout the domain of 0.3--10 AU for several specific theoretical examples. Our simulation unifies previous simulations which were limited to either the near-Sun region within 1 AU or the far region outside several AU. In addition, several new physical features and processes are revealed by this study, especially those concerning the global geometry and the detailed evolution of the corotating shocks. ¿ American Geophysical Union 1993