From Stretched String to GYRE

The numerical technique used in this chapter to solve the stretched-string BVP provides a strong analog to how GYRE solves the oscillation equations. The full, nasty details of GYRE’s approach are laid out in XXXX

In this section, let’s review the similarities and differences between the two.

Similarities

GYRE shares the following similarities to

  • Separation of variables
  • Discretization
  • Root bracketing for adiabatic
  • Root refinement
  • Failure scenarios

Differences in GYRE

  • More variables
  • Non-uniform spatial and frequency grids
  • The stretched string is discretized using a second-order form of the wave equation. GYRE breaks this up into 1st-order forms
  • The discretizaton scheme is more complex
  • Complex root solving for non-adiabatic