Laurent operator-based representation of discrete solutions in the Newmark scheme with non-homogeneous terms

This paper investigates representation results for second-order evolution equations arising in structural dynamics, discretized using the Newmark time integration scheme. More precisely, the discrete solution is expressed in terms of bi-infinite Toeplitz or Laurent operators.A spectral analysis of the associated discrete operators is discussed, and a convergence analysis is performed under relaxed regularity assumptions on the source term. Furthermore, we examine the errors introduced by some truncation strategies, including one that is commonly used in engineering practice.