Received

A truncation error analysis has been developed for the approximation of spatial derivatives in Smoothed Particle Hydrodynamics (SPH) and related first-order consistent methods such as the first-order form of the Reproducing Kernel Particle Method. Error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length, ∆x/h. For uniformly spaced particles in one dimension, analysis shows that as h is reduced while maintaining constant ∆x/h, error decays as h2 until a limiting discretisation error is reached, which is independent of h. If ∆x/h is reduced while maintaining constant h (i.e. if the number of neighbours per particle is increased), error decreases at a rate which depends on the kernel function’s smoothness. When particles are distribute