Summation by parts and truncation error matching on hyperboloidal slices

We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves mitigate outer boundary effects and, future, will help reduce systematic errors gravitational waveform extraction. also study a setup with truncation error matching. Our SBP-Stable scheme guarantees energy balance for class linear wave equations at semidiscrete level. develop specialized dissipation operators. The whole construction is made second-order accuracy spherical symmetry but could be straightforwardly generalized higher order or spectral without symmetry. In practical implementation, we evolve first scalar field obeying equation and observe, as expected, long-term norm convergence. obtain similar results potential term. To limitations approach, consider massive field, whose motion do not regularize dynamics near infinity, which involve excited incoming pulses cannot resolved code, very different massless setting. still observe excellent conservation, convergence satisfactory. Overall, our suggest compactified are likely provably effective whenever asymptotic solution space close equation.