Extension of Newman’s method to electrochemical reaction–diffusion in a fuel cell catalyst layer

A numerical technique is developed for solving coupled electrochemical reaction–diffusion equations. Through analyzing the nonlinearity of the problem, a trial and error iterating procedure is constructed. The coefficient matrix is arranged as a tridiagonal form with elements of block matrix and is decomposed to LU form. A compact forward and backward substitution algorithm based on the shift of inversing block matrix by Gauss–Jordan full pivoting is developed. A large number of node points is required to converge the calculation. Computation experiences show that the iteration converges very quickly. The effects of inner diffusion on the electrochemical reaction are analyzed by numerical solutions.