Computation of the frequency responses for distributed systems with one spatial variable

For a class of distributed systems with one spatial variable, we develop a method for computing the maximum singular value of the frequency response operator. This computation is typically done by resorting to finite-dimensional approximations of the underlying operators. In this paper, we introduce an alternative approach that avoids the need for numerical approximation of the operators in the evolution model. This involves two steps: (i) recasting the frequency response operator as a two point boundary value problem; and (ii) using state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. We provide an example from viscoelastic fluid dynamics to illustrate the utility of the proposed method.