Discretization methods for battery systems modeling

First principles battery models, consisting of nonlinear coupled partial differential equations, are often difficult to discretize and reduce in order so that they can be used by systems engineers for design, estimation, prediction, and management. In this paper, six methods are used to discretize a benchmark electrolyte diffusion problem and their time and frequency response accuracy is determined as a function of discretization order. The Analytical Method (AM), Integral Method Approximation (IMA), Padé Approximation Method (PAM), Finite Element Method (FEM), Finite Difference Method (FDM) and Ritz Method (RM) are formulated for the benchmark problem and convergence speed and accuracy calculated. The PAM is the most efficient, producing 99.5% accurate results with only a 3rd order approximation. IMA, Ritz, AM, FEM, and FDM required 4, 6, 9, 14, and 27th order approximations, respectively, to achieve the same error.