Bissell and Johnson [Phys. Fluids30, 779 (1987)] have calculated the electrostatic potential variation in the sheath and presheath regions of a collisionless plasma in which the source of ions is assumed to be Maxwellian. To do this, they imposed the generalized Bohm criterion as a boundary condition. In this paper the plasma equation is solved numerically without imposing the Bohm criterion as a boundary condition. The results compare well with their results. In addition, the ion distribution function throughout the plasma region is calculated. Because of this particular source model, the ion distribution at the center of the plasma has a spiked non‐Maxwellian shape.