In the smoothed particle hydrodynamics (SPH) method, the particle inconsistency problem significantly influences the calculation accuracy. In the present study, we investigate primarily the influence of the particle inconsistency on the first derivative of field functions and discuss the behavior of several methods of addressing this problem. In addition, we propose a new approach by which to compensate for this problem, especially for functions having a non-zero second derivative, that is less

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... computational demanding, as compared to the finite particle method (FPM). A series of numerical studies have been carried out to verify the performance of the new approach.