In this paper the combination of the Richardson extrapolation  with different numerical methods is studied to determine its advantages respect to tradditional methods, such as the trapezoidal integration commonly used in power system dynamic equations .
The simplest semi implicit method is the trapezoidal integration rule  that is based on Euler method by averaging the derivative values,
by trapezoidal integration method (Gabriel Filho et al.
obs] value was achieved by the trapezoidal integration method, Eq.
It also includes all of the same robust features found in previous versions, such as an option for trapezoidal integration
and a new time-step algorithm that result in a more accurate transient analysis, support for user defined functions in electrical and physical device parameters, and save and load commands to capture the state of a circuit simulation and continue from that point onward in a later simulation.