Relations between Transfer Matrices and Numerical Stability Analysis to Avoid the $\Omega d$ Problem

DOI10.1137/140993442zbMath1322.34097arXiv1503.09038OpenAlexW1692423489MaRDI QIDQ5261727

René Pernas-Salomón, V. R. Velasco, R. Pérez-Álvarez

Publication date: 7 July 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.09038

zbMATH Keywords

transfer matrixnumerical stabilitymatrix Sturm-Liouville problemquadratic eigenvalues\(\Omega d\) problem

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Sturm-Liouville theory (34B24) Linear ordinary differential equations and systems (34A30) Qualitative investigation and simulation of ordinary differential equation models (34C60) Waves and radiation in optics and electromagnetic theory (78A40) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16)

Related Items

Quantum thermostatted disordered systems and sensitivity under compression, Unitarity and symmetries of the multicomponent scattering matrix

Uses Software

• mctoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• On dispersion relations of waves in multilayered magneto-electro-elastic plates
• Three-dimensional Green's functions for infinite anisotropic piezoelectric media
• Wave propagation in magneto-electro-elastic multilayered plates
• Orthotropic elastic media having a closed form expression of the Green tensor
• The Quadratic Eigenvalue Problem
• Resolvent Method for Calculating Dispersion Spectra of the Shear Waves in the Phononic Plates and Waveguides
• Wave Impedance Matrices for Cylindrically Anisotropic Radially Inhomogeneous Elastic Solids
• A sextic formalism for three–dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials
• Accuracy and Stability of Numerical Algorithms