线性电路微分方程组小波配置法动态求解和仿真

Dynamic Solution and Simulation with the Wavelet Collocation Method for Differential Equation Series of the Linear Circuits

小波分析能否应用于微分方程的求解和仿真一直没有统一的定论。本文成功地将小波配置法引入线性电路微分方程组的动态求解和仿真,研究结果表明,它与常规的时域和频域方法相比具有以下的优点:1)由于小波基函数具有紧支撑的特点,需要相对较少的配置点就可以得到很好的仿真结果,仿真速度快;2)小波配置法本质上是基于时域的仿真分析,因此能很好的反映出电路的动态特性,从而为线性电路微分方程组的动态求解和仿真拓展了一种新的思路,也将为小波配置法进一步应用于非线性电路动态求解和仿真打下研究基础。

For a long period of time, it is not clear whether the wavelet can be used to solve and simulate all differential equation series or not. In this paper, wavelet collocation method for linear circuit simulation is proposed. Compared with methods in time or the frequency domains, wavelet collocation method has advantages as following: 1) with the characteristic of the compact support the simulation solution is found with relatively less collocation points and faster computational speed. 2) The proposed method is essentially based on the time domain so as to have excellent dynamic characteristics. It is a new methodology for the nonlinear circuit dynamic solution and simulation.