Analytic solutions to diffusion equations

The homotopy analysis method (HAM) is a promising method for handling functional equations. Recent publications have proved the effectiveness of the HAM in solving a wide variety of problems in different fields. In this work, through successfully applying the HAM for solving diffusion equations, we present examples which illustrate different procedures for controlling the convergence region of the solution series. Moreover, in all worked examples, we use the same auxiliary linear functional LL, the same auxiliary function HH and the same initial guess v0v0, which seems to be a good advantage.