Abstract The single-particle model is a useful mathematical representation for state-of-charge observation, parameter identification and control of lithium-ion batteries. This model is a simplified electrochemical formulation where ionic intercalation, described as a diffusive process, is considered as the dominant dynamics. In the search for a more efficient numerical solution of the involved partial differential equations, many approximations have been reported. However, most of them are valid just under restricted operating conditions. In this paper, spatial semidiscretization is reintroduced as the precision of approximations could be arbitrarily chosen with this approach. Three discretization methods are applied in a classical fashion, evaluated and compared in both time and frequency domains: finite difference, finite element and differential quadrature. In addition, two commonly used low order approximations are tested against semidiscretization approximations. The best results are obtained with the differential quadrature method in its polynomial version. Two model truncation criteria are also explored, one is based on bandwidth selection and the other on residue analysis, where the first resulted to be more conservative. Finally, simulations of representative reduced order approximations of the single-particle model are compared against experimental data found in the literature.