A stable method to solve the Matrix Sturm-Liouville Equation for inhomogeneous layered structures Articles uri icon

authors

  • PERNAS SALOMON, RENE
  • ARRIAGA, JESÚS
  • PÉREZ ÁLVAREZ, ROLANDO

publication date

  • December 2016

start page

  • 120

end page

  • 130

volume

  • 100

International Standard Serial Number (ISSN)

  • 0749-6036

Electronic International Standard Serial Number (EISSN)

  • 1096-3677

abstract

  • The study of elementary excitations in layered structures can be addressed via a Matrix Sturm-Liouville Equation of motion. A stable numerical method to solve this ubiquitous system of coupled second-order differential equations is presented. Its straightforward algorithm, especially useful for inhomogeneous layered structures, combines a local exponential approximation for the associated transfer matrix with the Hybrid matrix method. The latter is a well-known numerical stable method which is also useful to solve several boundary problems involving structures with planar, cylindrical or spherical geometry. Two numerical examples are considered and compared with the results reported previously to demonstrate the validity of the method.

subjects

  • Mathematics
  • Physics

keywords

  • stable numerical method; sturm-liouville equation; hybrid matrix; layered structures