publication . Preprint . Article . 2015

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

R. Pérez-Álvarez; R. Pernas-Salomón; V. R. Velasco;
Open Access English
  • Published: 02 Jul 2015
  • Country: Spain
Abstract
The transfer matrix method is usually employed to study problems described by $N$ equations of matrix Sturm--Liouville (MSL) kind. In some cases a numerical degradation (the so called $\Omega d$ problem) appears thus impairing the performance of the method. We present here a procedure that can overcome this problem in the case of multilayer systems having piecewise constant coefficients. This is performed by studying the relations between the associated transfer matrix $\boldsymbol{(T)}$ and other transfer matrix variants. In this way it was possible to obtain the matrices which can overcome the $\Omega d$ problem in the general case and then in problems which a...
Subjects
free text keywords: Mathematical Physics, 34L16, Transfer matrix, Ωd problem, Quadratic eigenvalues, Numerical stability, Matrix Sturm-Liouville problem, Matrix method, Matrix (mathematics), Mathematics, Transfer-matrix method (optics), Mathematical optimization, Boundary value problem, Constant coefficients, Mathematical analysis, Piecewise
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publication . Preprint . Article . 2015

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

R. Pérez-Álvarez; R. Pernas-Salomón; V. R. Velasco;