随着工业及其它产业应用，如机械臂控制，对求解的实时性、精度等要求越来越高，将问题建模为静态/时不变形式难以满足需求。研究未来时变问题不仅符合时代特点，而且具有前瞻性和便于数字计算与应用。本项目研究高精度时间离散公式与神经动力学，并以之为基础研究未来时变问题的求解。也即，依据未来时变离散问题的隐动态性，将问题做连续化处理，再通过应用神经动力学得到连续求解模型；之后，将连续求解模型做离散化处理，通过设计与应用高精度时间离散公式而得到离散求解模型。最后，理论分析模型稳定性、收敛性等，并开展计算机数值实验验证。本项目拟深入研究未来时变问题求解，重点为：1系统地提出更高精度时间离散公式与通式，以提高求解精度和解模型的多样性；2研究更复杂的未来时变问题甚至是不同层未来时变问题，以满足复杂工业产业问题的建模与求解需求；3对比性研究各离散时间求解模型的各类性质，如鲁棒性、升阶情况等，以提高实用性和优越性。

With the increasing desire of real-time performance and precision for industrial applications, such as robot manipulator control, it is not enough to formulate the problems as static / time-invariant forms. The study of future time-varying problems (i.e., discrete time-varying problems) not only meets the current requirements, but also facilitates the numerical computations and applications. This project studies future time-varying problems solving on the basis of high-precision time-discretization formulas and neural dynamics. That is, according to the feature of the implicit dynamics of future time-varying discrete problems, we make the continuation treatment of the original problems, and the continuous solution models are obtained by applying neural dynamics; then, we make the discretization treatment of the continuous solution models, and the discrete solution models are obtained by designing and applying high-precision time-discretization formulas. Finally, we analyze the stability and convergence, and substantiate the results by computer experiments. The project will conduct in-depth studies of future time-varying problems, focusing on the following: 1) time-discretization formulas with higher precision and their general forms would be proposed and investigated systematically to enhance the solution precision and the solution-model diversity; 2) more complicated future time-varying problems and even different-level problems would be studied to satisfy the requirements of modeling and solution of complicated industrial problems; 3) many properties, such as robustness and order-increasing situation, of various discrete-time solution models would be analyzed and investigated comparatively to enhance the practicability and superiority.