Advantages of the Complex Taylor Series Expansion Method for determining Circuit Outputs

The complex Taylor series expansion (CTSE) is a method to compute derivatives numerically with machine precision for real valued functions. This method converts a real-valued function to complex-valued and introduces a small imaginary step to the parameter of interest. In this work, CTSE had been used in an electrical circuit to find the current flowing through a capacitor with respect to the voltage across the capacitor, where the voltage across the capacitor is a complicated solution of a differential equation. The advantage of CTSE is that it can be used to find accurate derivatives of arbitrary functions. A limitation of CTSE is that it can only be used to compute the first order derivative of a function. A numerical example is presente to demonstrate the accuracy of the method.