Accurate gravitational wave calculations from the Regge-Wheeler equation in the time domain

We calculated the energy flux emitted by an extreme mass-ratio inspiral. To do this, we solved the Regge-Wheeler equation in the time domain using the method of lines and numerically integrating; a fourth-order finite difference method was used to increase accuracy. We used Regge-Wheeler source terms to represent the source by enforcing a jump condition across an internal boundary at the source position. We also made use of a hyperboloidal slicing and compactification scheme, based on the work of Thornburg and Wardell (2017). With a fourth-order finite difference method and exact compactified boundary conditions, we hope to achieve results that are among the most accurate time domain calculations.