In this paper we blend high-order Compact Approximate Taylor (CAT) numerical methods with the a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of conservation laws. The resulting methods are highly accurate for smooth solutions, essentially non-oscillatory for discontinuous ones, and almost fail-safe positivity preserving. Some numerical results for scalar conservation laws and systems are presented to show the appropriate behavior of CAT-MOOD methods.

翻译：本文将高阶紧致近似泰勒(CAT)数值方法与后验多维最优阶检测(MOOD)范式相结合，以求解一维守恒律的双曲系统。所得方法对于光滑解具有很高的精度，对于不连续解几乎没有震荡，并且几乎是失效安全的正性保持。通过一些标量守恒律和系统的数值结果，展示了CAT-MOOD方法的适当行为。