The talk is aimed to study numerical issues related to the stochastic extension of a morphochemical reaction-diffusion model for batteries, denoted as DIB model. In this model, recharge instability is controlled by the interaction between material shape (morphology) and material chemistry. The effects of adding stochastic source terms on the overall dynamics are analysed under a numerical point of view. In particular, the talk aims to understand the effects of stochasticity on Turing patterns for the dynamics of the stochastic DIB. Conditions for the formation of Turing patterns are studied, studying for those characterizing the deterministic DIB model, by means of perturbation theory arguments. Theoretical issues are then confirmed by the numerical evidence. This talk fully falls within the activities of the PRIN-PNRR project P20228C2PP BAT-MEN (BATtery Modeling, Experiments & Numerics) - Enhancing battery lifetime: mathematical modeling, numerical simulations and AI parameter estimation techniques (CUP: E53D23017940001). REFERENCES [1] Bozzini B., Lacitignola D., Mele C. et al. Coupling of morphology and chemistry leads to morphogenesis in electrochemical metal growth: a review of the reaction-diffusion approach. Acta Appl. Math. 12, 53-68 (2012). [2] D’Ambrosio R. Numerical approximation of ordinary differential problems - From deterministic to stochastic numerical methods, Springer (2023). [3] Lacitignola D., Bozzini B., Frittelli M., Sgura I. Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition, Comm. Nonlin. Sci. Numer. Simul. 48, 484-508 (2017). [4] Lacitignola D., Bozzini B., Peipmann R., Sgura I. Cross-diffusion effects on a morphochemical model for electrodeposition, Appl. Math Mod. 57, 492-513 (2018). [5] Lacitignola D., Bozzini B., Sgura I. Spatio-Temporal Organization in a Morphochemical Electrodeposition Model: Hopf and Turing Instabilities and their Interplay, Eur. J. Appl. Math. 26, 143-173 (2015).