Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

An investigation of the Runge-Kutta time-stepping, combined with compact difference schemes to solve the unsteady Euler equations, is presented. Initially, a generalized form of a N-step Runge-Kutta technique is derived. By comparing this generalized form with its Taylor's series counterpart, the criteria for the three-step and four-step schemes to be of third- and fourth-order accurate are obtained.