A computer solver using the Adomian decomposition method to solve non-linear electrochemical models has been developed. The explicit solutions for two kinds of models, for a solid polymer electrolyte direct methanol fuel cell and a packed bed reactor, were obtained and compared with the solutions supplied by an ordinary numerical method. Convergence and convergent radius of non-linear models are discussed. A piecewise solution technique is suggested to overcome the divergent difficulty and enlarge the application range of the solver.