Alternative analytical solutions of the diffusion (thermal conductivity) equation for an arbitrary initial concentration (temperature) distribution

Alternative analytical solutions of the diffusion (or thermal conductivity) equation are presented, which ensure rapid convergence even for small values of Dt/l ² (αt/l ²), where D is the diffusion coefficient, α 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).