Moments and the quadrature approximation

Given the analytical solution, it is straightforward to compute the integer moments using the definition 

Likewise, the quadrature approximation can be found from these moments. For example, for a one-node quadrature the weights and abscissas are defined by 

Note that due to the hyperbolic form of the kinetic equation, the moments, weights, and abscissas need not be smooth functions of x. For simplicity, we will consider the moments for two cases. The first uses a continuous initial NDF defined by fi=fi = [o,i]( ), and the second a discrete NDF defined by /i = 6( - /2) and /2 = 6( - 3 /2). 

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