Cesur, Yusuf2021-06-232021-06-232010978-0-7354-0863-00094-243Xhttps://hdl.handle.net/20.500.12491/6800https://doi.org/10.1063/1.3525113International Conference on Mathematical Sciences -- NOV 23-27, 2010 -- Abant Izzet Baysal Univ, Bolu, TURKEYIn this paper we consider the solution of a linear second-order differantial equation Ay '' + By' + Cy = f(t) where A, B, and C are n x n Toeplitz matrices with sign changes real entries and y(t) is an nth-ordei vector. We show that the solution can be expressed in terms of the eigensolution of the corresponding Quadratic Eigenvalue Problem (QEP) and explain why eigenvalues and eigenvectors give useful information. Also we give some examples for Quadratic Polynomials (quadratic matrix polynomial) and their epsilon - pseudospectra. Computed examples of pseudo-spectra an presented throughout, with using Mathematica, and applications in numerical analysis are mentioned.eninfo:eu-repo/semantics/closedAccessQuadratic Eigenvalue ProblemEigenvalueEigenvectorMatrix PolynomialSecond-order Differantiol EquationSpectrumEpsilon - PseudospectrumConference Object13091931992-s2.0-79251556242N/AWOS:000287125700021N/A