Numerical method for the analysis of time-varying singular systems

A new method that generates approximate values of the solution of the time-varying singular problem is presented. The method of regularisation is used to overcome the ill-posedness of this problem and a relation between the unknown state variable and its derivative is generated. A pseudospectral method is used to discretise this relationship. The discrete relationship between the state variable and its derivative is reduced to a set of algebraic equations, which are solved to produce values of the state variable at discrete values of time. Performance of this method is evaluated through its application to the solution of an example of a time-varying singular system. Results from this example show that this method generates excellent approximate values for the state variable of the singular system