Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one-dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton-GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES (m) and preconditioned with Incomplete Lower-Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)-GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES (m) algorithm on the computation time was revealed; in particular, they were able to speed up the program.

Software-defined networking (SDN) requires adaptive control strategies to handle dynamic traffic conditions and heterogeneous network environments. Reinforcement learning (RL) has emerged as a promising solution, yet deep RL methods often face instability, non-stationarity, and reproducibility challenges that limit practical deployment. To address these issues, a kernel-based RL framework is introduced, embedding transition dynamics into reproducing kernel Hilbert spaces (RKHS) and combining kernel ridge regression with policy iteration. This approach enables stable value estimation, enhanced sample efficiency, and interpretability, making it suitable for large-scale and evolving SDN scenarios. Experimental evaluation demonstrates consistent convergence and robustness under traffic variability, with cumulative rewards exceeding those of baseline deep RL methods by more than 22%. The findings highlight the potential of kernel-embedded RL as a practical and theoretically grounded solution for adaptive SDN management and contribute to the broader development of intelligent systems in complex environments.