一类具有时滞的非线性微分代数系统的谱方法

Spectral Method for Nonlinear Differential-algebraic Equations with Delays

首先给出了一类带有时滞的非线性微分代数系统(DDAE)存在惟一解的充分条件:然后将原问题变形为无时滞的带有非局部边值条件的偏微分系统;接下来运用Chebyshev谱方法求得原问题的近似解。所用方法的优点在于避免了许多在处理时滞项时所遇到的数值困难,而且谱方法具有高精度;最后,给出了实例来说明所提出的方法的可行性。

We firstly investigate the solvability of nonlinear differential-algebraic equations with delays; furthermore, the orginal problem is translated to a partial differential equations without delays under nonlocal boundary conditions. The approximation solution is obtained by using Chebyshev pesudospctral method, the advantages of which are avoiding many of the numerical difficulties in dealing with the delays and high accuracy. A numerical example is given to illustrate the theoretical result.