The relaxation process of a space uniform plasma composed of cold electrons and one species of hot ions is studied numerically using one- and two-dimensional Landau–Fokker–Planck codes. Relaxation of a monoenergetic ion beam is considered in possibly extreme temperature regimes. Special attention is paid to the deviation of the relaxation process from the classical picture, which is characterized by the close initial temperaturesTe≫(me/mi)1/3Ti.The present results give quite a clear idea of the relaxation picture for any initial temperatures also in extreme temperature regimes. A difference scheme, preserving the number of particles and the energy, gives the possibility of solving the problem numerically without error accumulation, except for machine errors. ©1998 American Institute of Physics.