Question about the numerical method used for solving Exchange Rate Disconnect in General Equilibrium


I’m expanding the model presented in “Exchange Rate Disconnect in General Equilibrium.” The authors’ online Appendix does not include the linearized equilibrium conditions of the full-fledged model, which, however, are given in their provided MatLab code. I struggle to comprehend their code because I don’t know their numerical method. I would appreciate it if someone could tell me which method they are using to solve the model (and attach some references for the method) and give me some advice on how to extract the equilibrium conditions from their code. I have attached their code for your reference. Thanks a lot.
replication_code.m (12.3 KB)

This looks like first order perturbation with them solving the resulting quadratic matrix equation using the Jordan Eigenvalue decomposition to diagonalize the transition matrix.

Thank you, Dr. Pfeifer. Now I have figured out the equilibrium conditions.