Our current society is going through a period of multiple challenges, such as wars, economic crisis, climate changes. The latter problem has encouraged researchers to find new sources of renewable energy or to improve the existing ones. An example is represented by studies recently made to extend the life of batteries. During charging and discharging processes, the formation of metallic materials inside their structures may occur, leading to a related deterioration. In these situations, mathematical models like the DIB morpho-chemical model [2], based on a system of reaction-diffusion 2D partial differential equations (PDEs) can be employed. To accurately reproduce the mentioned formation of metallic materials, the DIB model requires numerical integration over large time intervals, and the use of very fine meshes for the space discretization. The calibration of the model to fit real data by means of optimization or AI techniques, typically requires solving the PDE multiple times. Therefore, the employment of efficient and stable time integrators combined with suitable space discretizations is needed. The main aim of this talk is to present new matrix-oriented W-methods of high order for the efficient solution of reaction-diffusion PDEs like the DIB model. We also compare the new matrix-oriented W-methods with the so-called AMF-W (Alternate Matrix Factorization with inexact Jacobian) splitting schemes [1, 3], particularly suitable for systems of parabolic PDEs defined in several space dimensions. We then analyze the properties of both classes of methods, discussing their advantages depending on the problem to be solved. This Minisymposium falls within the activities of PRIN PNRR 2022 project P20228C2PP BAT-MEN (CUP: F53D23010020001), granted by the Italian Ministry of University and Research. REFERENCES [1] Conte, D., González-Pinto, S., Hernández-Abreu, D., and Pagano, G. On approximate matrix factorization and TASE W-methods for the time integration of parabolic partial differential equations. J. Sci. Comput., (2024). 100(2), 34. [2] D’Autilia, M. C., Sgura, I., and Simoncini, V. Matrix-oriented discretization methods for reaction–diffusion PDEs: Comparisons and applications. Comput. Math. Appl., (2020) 79.7: 2067-2085. [3] González-Pinto, S., Hernández-Abreu, D., and Pérez-Rodríguez, S. W-methods to stabilize standard explicit Runge–Kutta methods in the time integration of advection–diffusion–reaction PDEs. J. Comput. Appl. Math., (2017) 316: 143-160.