A computational study is undertaken of traveling wave current drive based on the nonlinear interaction between radio-frequency components of the current and magnetic field induced in a plasma. Results are presented which describe the current drive in the Synchromak (m=0), double helix (m=1) and, in particular, the computationally more complex helical mesh (m=+1 and m=-1) experiments. A general technique for the numerical solution for the driven currents is developed which includes Fourier harmonics to arbitrary order for this variety of external coil structures. By adjusting the relative currents in the helical mesh external coils, considerable flexibility in the control of both poloidal and toroidal current drive results.