Abstract:

The homotopy analysis method was presented (short: HAM) for obtaining numerical solutions of a diffusion equation with boundary conditions. The series solution was developed and the recurrence relations were explicitly given. The initial approximation can be freely chosen with possible unknown constants, which can be determined by imposing the boundary and initial conditions. The HAM contains the auxiliary parameter h, which can provide a simple way to adjust and control the convergence region of solution series. Comparisons were made between the HAM, the exact solution and the other method. The results revealed that the HAM is  effective and simple.

Key words: diffusion equation; homotopy analysis method; Crank-Nicolson scheme