Galerkin Approximations for Thermoacoustic Instability in a Rijke's Tube

A simple mathematical model for thermoacoustic instability (TAI) in a Rijke's tube results in a first-order neutral delay differential equation (NDDE). In this work, the NDDE governing the TAI is converted to a partial differential equation (PDE) and then into a system of ordinary differential equations (ODEs) using Galerkin approximations. A new pseudo inverse method, is proposed to handle the boundary conditions in the Galerkin method. The stability results obtained using our method are validated using the data from the literature.