Advection-diffusion-reaction systems of Partial Differential Equations (PDEs) frequently arise in sustainability models, including vegetation dynamics in arid environments, corrosion processes, and battery degradation during charge/discharge cycles. These models are often defined over large spatial domains and are characterized by stiffness, oscillatory behaviors, and positivity constraints. Therefore, stable, accurate, and computationally efficient numerical methods are essential for their solution. In this talk, we present new time-integration techniques inspired by the so-called Time-Accurate and highly-Stable Explicit (TASE) operators [1, 2]. In particular, we explore the connections between TASE based Runge-Kutta methods and Rosenbrock and W-methods, and exploit them to derive highly efficient numerical schemes for large stiff initial value problems (IVPs) arising from the spatial semi-discretization of advection-diffusion-reaction PDEs. Furthermore, for two-dimensional parabolic PDEs, we employ suitable spatial splitting approaches that further reduce the computational cost of the proposed methods, while preserving their order of convergence [3, 4]. Numerical experiments on models of vegetation dynamics and battery degradation show the efficiency of the new methods. Their potential for use in parameter calibration from real data is also discussed. Acknowledgements: This research falls within the activities of PRIN-MUR 2022 project 20229P2HEA Stochastic numerical modelling for sustainable innovation (CUP: E53D23017940001), granted by the Italian Ministry of University and Research within the framework of the call relating to the scrolling of the final rankings of the PRIN 2022 call. REFERENCES [1] L. Aceto, D. Conte, G. Pagano. Modified TASE Runge-Kutta methods for integrating stiff differential equations. SIAM J. Sci. Comput. 47(3) (2025). [2] D. Conte, J. Martin-Vaquero, G. Pagano, B. Paternoster. Stability theory of TASE-Runge-Kutta methods with inexact Jacobian. SIAM J. Sci. Comput. 46(6) (2024). [3] D. Conte, S. Gonz´ alez-Pinto, D. Hern´ andez-Abreu, G. Pagano. On Approximate Matrix Factorization and TASE W-methods for the time integration of parabolic Partial Differential Equations. J. Sci. Comput. 100 (2024). [4] S. Gonzalez-Pinto, D. Hernandez-Abreu, G. Pagano, S. Perez-Rodriguez. Generalized TASE-RK methods for stiff problems. Appl. Numer. Math. 188 (2023).