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In this paper, a core-shell enhanced single particle model for iron-phosphate battery cells is formulated, implemented, and verified. Starting from the description of the positive and negative electrodes charge and mass transport dynamics, the positive electrode intercalation and deintercalation phenomena and associated phase transitions are described with the core-shell modeling paradigm. Assuming two phases are formed in the positive electrode, one rich and one poor in lithium, a core-shrinking problem is formulated and the phase transition is modeled through a shell phase that covers the core one. A careful discretization of the coupled partial differential equations is proposed and used to convert the model into a system of ordinary differential equations. To ensure robust and accurate numerical solutions of the governing equations, a sensitivity analysis of numerical solutions is performed and the best setting, in terms of solver tolerances, solid phase concentration discretization points, and input current sampling time, is determined in a newly developed probabilistic framework. Finally, unknown model parameters are identified at different C-rate scenarios and the model is verified against experimental data.