Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable methods to solve the impedance matrix for radially inhomogeneous
  cylindrically anisotropic structures   A stable approach for integrating the impedance matrix in cylindrical, radial
inhomogeneous structures is developed and studied. A Stroh-like system using
the time-harmonic displacement-traction state vector is used to derive the
Riccati matrix differential equation involving the impedance matrix. It is
found that the resulting equation is stiff and leads to exponential
instabilities. A stable scheme for integration is found in which a local
expansion is performed by combining the matricant and impedance matrices. This
method offers a stable solution for fully anisotropic materials, which was
previously unavailable in the literature. Several approximation schemes for
integrating the Riccati equation in cylindrical coordinates are considered:
exponential, Magnus, Taylor series, Lagrange polynomials, with numerical
examples indicating that the exponential scheme performs best. The impedance
matrix is compared with solutions involving Buchwald potentials in which the
material is limited to piecewise constant transverse isotropy. Lastly a
scattering example is considered and compared with the literature.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ