Solution operator approximations for characteristic roots of delay differential equations
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Numerical detection of instability regions for delay models with delay-dependent parameters
Journal of Computational and Applied Mathematics
Automatica (Journal of IFAC)
Efficient computation of characteristic roots of delay differential equations using LMS methods
Journal of Computational and Applied Mathematics
Automatica (Journal of IFAC)
Characterization and Computation of $\mathcal{H}_{\infty}$ Norms for Time-Delay Systems
SIAM Journal on Matrix Analysis and Applications
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
SIAM Journal on Control and Optimization
Journal of Computational and Applied Mathematics
Root locus for SISO dead-time systems: A continuation based approach
Automatica (Journal of IFAC)
Krylov-Based Model Order Reduction of Time-delay Systems
SIAM Journal on Matrix Analysis and Applications
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In [D. Breda, S. Maset, and R. Vermiglio, IMA J. Numer. Anal., 24 (2004), pp. 1--19.] and [D. Breda, The Infinitesimal Generator Approach for the Computation of Characteristic Roots for Delay Differential Equations Using BDF Methods, Research report UDMI RR17/2002, Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Udine, Italy, 2002.] the authors proposed to compute the characteristic roots of delay differential equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge--Kutta (RK) and linear multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based on pseudospectral differencing techniques. We prove the "spectral accuracy" convergence behavior typical of pseudospectral schemes, as also illustrated by some numerical experiments.