New Kernel Function for the Approximation of Third Order Derivatives

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Yaiche Ilham

Abstract

A new kernel function is developed to approximate the third order derivative by mean of the Smoothed Particle Hydrodynamics (SPH) method. It has the advantage to be efficiently used with gridded data and random distributions. Due to the discrepancy of the particles in the former distribution, we extended the use of the CSPM method for the approximation of third order derivatives. Our new kernel function provides three accurate numerical schemes, in conjunction with the trapezoidal rule, Simpson’s rule and the CSPM method respectively.

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