The existing discrete-time neural dynamics methods for solving the multi-linear tensor equation (MTE) with \(\mathcal {M}\) -tensor are all derived from the continuous-time one and depend on the Euler difference formula, which cannot apply to essentially discrete problems and have low solution accuracy. Moreover, these methods all focus on static problems, not consider time-varying ones, and thus may have unsatisfactory performance in applications with time-varying parameters. Additionally, most of these methods fail to handle the MTE with \(\mathcal {M}\) -tensor under noisy conditions. To remedy these issues, a high-order robust discrete-time neural dynamics (HRDND) method with a directly discrete approach is given for solving the time-varying MTE (TMTE) with \(\mathcal {M}\) -tensor in this chapter. Theoretical analyses on convergence and robustness are provided to prove that the proposed HRDND method is feasible and effective. Finally, simulative experiments on two time-varying numerical examples and an application derived from the Bellman equation solved by the proposed HRDND method and other four methods are given, whose results illustrate the superiority of the proposed HRDND method.