With the aim of modelling the formation of spatio-temporal patterns in battery electrodeposition, we consider the well-established DIB (Dual-Ion Batteries) model [1], consisting of a 2D reaction-diffusion Partial Differential Equations (PDEs) system, which couples an equation for the morphological dynamics with one for the surface chemical dynamics. The aim of this talk is to investigate the effects of stochasticity on the overall dynamics, by employing adapted numerical methods for the resulting stochastic PDE. The numerical treatment of this problem requires the employment of non-trivial techniques, since a related spatial discretization performed e.g. via finite differences, finite elements, or spectral methods, leads to a large and highly stiff system of Stochastic ordinary Differential Equations (SDEs). We derive new classes of efficient linearly implicit methods for SDEs by using the so-called Time-Accurate and highly-Stable Explicit (TASE) preconditioners [2, 3, 4, 5]. Numerical experiments show that the new methods efficiently solve the stochastic DIB model, employing reasonable computing times, and permitting to analyse the effects of stochasticity on the formation of Turing patterns. This talk is part of a research activity within the project PRIN PNRR 2022 P20228C2PP (CUP: F53D23010020001) BAT-MEN (BATtery Modeling, Experiments & Numerics). [1] B. Bozzini, D. Lacitignola, and I. Sgura. Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation. J Solid State Electrochem., 17, 467–479, 2013. [2] M. Calvo, J. I. Montijano, and L. Randez. A note on the stability of time-accurate and highly-stable explicit operators for stiff differential equations. J. Comput. Phys., 436:Paper No. 110316, 13, 2021. [3] D. Conte, J. Martin-Vaquero, G. Pagano, and B. Paternoster. Stability theory of TASE-Runge-Kutta methods with inexact Jacobian. SIAM J. Sci. Comput., accepted for publication. [4] D. Conte, G. Pagano, and B. Paternoster. Time-accurate and highly-stable explicit peer methods for stiff differential problems. Commun. Nonlinear Sci. Numer. Simul., 119, 20, 2023. [5] D. Conte, G. Pagano, and B. Paternoster. Nonstandard finite differences numerical methods for a vegetation reaction-diffusion model. J. Comput. Appl. Math., 419:Paper No. 114790, 17, 2023.