本文用多层前向神经网络求解该非线性偏微分方程，从而逼近非线性系统的中心流形。
In this paper, multi-layer feedforward neural networks are used to solve the nonlinear partial differential equation, and approach the centre manifold of the nonlinear system.
仿真结果表明，用本文提出的简化模型能较好地逼近基于偏微分方程的严格模型，且结构简单，易于应用。
Simulation results show that the simplified model provided by this method can satisfactorily imitate rigorous model in addition to its simple structure and feasibility for on line applications.
第二节介绍用三次矩阵样条函数方法逼近一阶矩阵非线性微分方程的数值解。
Section II describes the numerical solution of first-order matrix differential non-linear equation using the cubic matrix spline function.
对三维波动方程做单程波分解，给出了用低阶偏微分方程组逼近上行波方程的2种高阶近似表达式。
This paper performs one-way wave decomposition for 3d wave equation, and 2 kinds of high approximation of up-going wave equation in low order differential equation system are derived.
对三维波动方程做单程波分解，给出了用低阶偏微分方程组逼近上行波方程的2种高阶近似表达式。
This paper performs one-way wave decomposition for 3d wave equation, and 2 kinds of high approximation of up-going wave equation in low order differential equation system are derived.
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