A core physics-based model for PEM fuel cell impedance reduces to the numerical solution of a boundary value problem for two coupled, linear, complex–valued ordinary differential Eqs. with variable coefficients. We report a matrix formulation of a previously developed recurrent method for the fast numerical solution of this problem. This formulation does not require iterations and it utilizes only elementary functions and 4 × 4 matrix products, resulting in one to two orders of magnitude faster code compared to the standard Python boundary–value problem solver. This significantly improves the computational speed of the physics-based impedance model, making it competitive with the popular equivalent circuit modeling approach. The numerical calculation of cell impedance is demonstrated based on the model that includes proton transport in the catalyst layer and oxygen transport in the catalyst and gas-diffusion layers. Least–squares fitting of a real experimental spectrum shows that the matrix solver returns the cell transport parameters 50 times faster than the classic boundary–value problem solver.
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