A New Numerical Approach to Transfer Functions of LTI-PDEs

In the present paper, we introduce a new approach for the numerical calculation of transfer functions of linear time-invariant partial differential equations in a non-parametric form, e.g. for a subsequent approximation using (non-) rational transfer functions. With the approach, the closed-form solution of the transfer function is represented using a state transition matrix. Thus, the value of the transfer function at explicit values of the complex frequency can be determined by numerically solving the matrix differential equation of the former. The idea is illustrated using an example. In addition, a comparison with the system’s closed-form solution is carried out and the advantages of the new approach over an established one based on a finite-dimensional approximation are shown.