Alternative analytical solutions of the diffusion (or thermal conductivity) equation are presented, which ensure rapid convergence even for small values of Dt/l(2) (alphat/l(2)), where D is the diffusion coefficient, alpha is the thermal diffusivity, t is the time, and l is the characteristic size. The solutions possess a general character and are valid for an arbitrary initial distribution of the concentration (temperature). (C) 2002 MAIK "Nauka / Interperiodica".