In this work, we first derive the evolution equation for the general energy-momentum moment of $\delta f$, where $\delta f$ is the deviation from the local equilibrium phase-space density. We then introduce a relativistic extension of regularized hydrodynamics developed in the nonrelativistic case by Struchtrup and Torrilhon that judiciously mixes the method of moments and Chapman-Enskog expansion. Hydrodynamic equations up to the third-order in gradients are then systematically derived within the context of a single species system and the relaxation-time approximation. This is followed by a series of linear stability and causality analysis. For the massless particles without any charge conservation, the third-order hydrodynamics is shown to be linearly stable and causal.

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• Hydrodynamic models
• Kinetic theory
• Relativistic heavy-ion collisions
• Transport in heavy-ion collisions