In perspective of global approximation, this study presents a numerical method for the generalized density evolution equation (GDEE) based on spectral collocation. A sequential matrix exponential solution based on the Chebyshev collocation points is derived in consideration of the coefficient or velocity term of GDEE being constant in each time step, then the numerical procedure could be successively implemented without implicit or explicit difference schemes. The results of three numerical examples indicate that the solutions in terms of the sequential matrix exponential method for GDEE have good agreement with the analytical results or Monte Carlo simulations. For sufficiently smooth cases, there need no more than one hundred representative points to achieve a satisfied solution by the proposed method, whereas for the case in presence of severe discontinuity a few more sampling points are required to keep numerical stability and accuracy.

从全局逼近的角度，本研究提出了一种基于频谱搭配的广义密度演化方程（GDEE）的数值方法。考虑到GDEE的系数或速度项在每个时间步都是恒定的，得出了基于Chebyshev配置点的顺序矩阵指数解，然后可以连续执行数值过程而无需隐式或显式差分方案。三个数值算例的结果表明，针对GDEE的顺序矩阵指数法的解与解析结果或蒙特卡洛模拟具有很好的一致性。对于足够平滑的情况，通过所提出的方法获得不超过100个代表点即可获得满意的解决方案，