Numerical Methods

This chapter explains the numerical methods used by the gyre frontend to solve the oscillation equations (similar approaches are followed in other frontends). Although it aims to be user-friendly, gyre is nevertheless a complex piece of software; thus, getting it to produce the ‘best’ results requires some degree of insight into the algorithms it uses to calculate mode eigenfrequencies and eigenfunctions.

• The Stretched String Problem
  • Analytic Solution
  • Separation
  • Discretization
  • Linear System
  • Scanning for Eigenfrequencies
  • Eigenfunction Reconstruction
• From Stretched String to gyre
  • Separation
  • Discretization
  • Linear System
  • Scanning for Eigenfrequencies
• Limitations of the Numerical Method
  • Insufficient Spatial Resolution
  • Insufficient Frequency Resolution