Multi-moment ADER-Taylor methods for systems of conservation laws with source terms in one dimension

HWENO accuracy was generally equal to or better than a five-moment MM-Loc scheme. MM-Loc was less accurate than RKDG at lower refinements, but with greater h- and p-convergence, RKDG accuracy is eventually surpassed. The ADER time integrator of MM-Loc also proved more accurate with p-refinement at a CFL of unity than a semi-discrete RK analog of MM-Loc. Being faster in serial and requiring less frequent inter-node communication than Galerkin methods, the ADER-based MM-Loc and HWENO schemes can be spatially refined and have the same runtime, making them a competitive option for further investigation.