In the cylindrical coordinate, the origin r = 0 plays a role of the singularity and thus much care is needed to treat near-origin region. This work presents a new numerical scheme which is derived from the exact solution under the one-dimensional assumption in the radial direction. It is shown that the near-origin region can be properly treated by the radial-exponential scheme, whereas the numerical results from the conventional exponential scheme deviate considerably from the exact solution. Over the region of small ($ {delta}r_e/r_e$ the present radial-exponential scheme turns out to be almost the same as the exponential scheme