Analyzing the Stability of Compact Finite Difference Schemes for Use in Binary Black Hole Simulations

There is a growing need to produce highly accurate and stable simulations for binary black hole mergers. Merger simulations with large mass ratios and large spins on highly eccentric orbits require significantly more computational resources than current evolutions and algorithms can manage. We propose to reduce some of these costs by using compact finite difference (CFD) schemes. We discuss methods in developing stable CFD schemes for both first and second derivatives with physical boundary conditions. We present our progress on finding a family of such schemes and the techniques we use to verify that these schemes are indeed stable and provide improved accuracy for future binary black hole simulations.