A pseudoimplicit predictor-cor rector relaxation algorithm with five-point central differencing in space has been developed for the solution of the governing differential equations of the helicopter rotor free-wake problem. This new approach is compared and contrasted with more conventional explicit-type free-wake algorithms. A convergence analysis shows that the new algorithm provides for much more rapid convergence characteristics compared to explicit methods, with improvements in numerical efficiency and predictive accuracy. Nomenclature be = spatial boundary condition vector CT = rotor thrust coefficient, Tlp7rR2([lR)2 c = blade chord, m E — shift operator i,/, k = unit vectors in the x, y, and z directions, respectively L = spatial discretization operator / = length of discretized vortex element, m Nh = number of blades N.t. = number of vortex filaments P = iteration scheme operator R = rotor radius, m r(. = vortex core radius, m r, = spanwise location from which vortex filaments are trailed, m r = position vector of a point on a vortex filament, m S = source vector T = rotor thrust, N / = time, s V.,_ — freestream velocity, m/s V = time invariant flowfield velocity, m/s Vind = induced velocity, m/s Vloc = local velocity at a point in space, m/s VH = tangential velocity, m/s Cartesian coordinate system, origin at hub center rotor shaft angle (negative forward), deg )3() = blade coning angle, deg r = circulation, m2/s Ar" = nth iteration position-vector correction f = distance along trailed wake filament (wake age), rad A.- = uniform-induced inflow ratio