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This work investigates the problem of future linear equation system under various noises. Firstly, a continuous advanced zeroing neurodynamic (CAZN) model under noise is developed to solve continuous linear equation system. Subsequently, by combining a general explicit linear left–right four-step (ELLRFS) formula with the CAZN model, a general ELLRFS discrete advanced zeroing neurodynamic (ELLRFS-DAZN) algorithm under noise is proposed to solve the future linear equation system. Theoretical analyses and results manifest the convergence performance of the general ELLRFS-DAZN algorithm under various noises. Moreover, numerical experimental results, including those based on a UR5 manipulator, validate the effectiveness and robustness of the general ELLRFS-DAZN algorithm under various noises. Numerical experimental results based on mobile acoustic source localization further substantiate the superiority of the general ELLRFS-DAZN algorithm under constant noise. Finally, physical experimental results based on a Kinova JACO2 manipulator substantiate the practicability of the general ELLRFS-DAZN algorithm under bounded random noise. [ABSTRACT FROM AUTHOR]