Numerical simulations of relativistic magnetohydrodynamics are essential for understanding astrophysical problems like binary neutron star mergers, accretion onto a black hole, and core collapse supernova explosions. To date, such simulations use low-order numerical methods that do not guarantee physical requirements such as positivity of the pressure and density. These simulations are computationally expensive because of the high resolution they need. High-order methods allow for improved accuracy at lower resolutions, making for cheaper and more accurate simulations. I will give an overview of the next-generation astrophysics code, SpECTRE (github.com/sxs-collaboration/spectre), and the novel numerical methods being employed. SpECTRE uses discontinuous Galerkin methods combined with adaptive-order finite-difference methods to achieve high-order accuracy and robust shock capturing, while guaranteeing positivity preservation. Additionally, these numerical methods are well-suited for task-based parallelism, which SpECTRE uses to achieve efficient scaling to exascale supercomputers.