Evaluation of the use of the Chebyshev algorithm with the quadrature method of moments for simulating aerosol dynamics

The quadrature method of moments (QMOM) has been widely used for the simulation of the evolution of moments of the aerosol general dynamic equations. However, there are several shortcomings in a crucial component of the method, the product-difference (P-D) algorithm. The P-D algorithm is used to compute the quadrature points and weights from the moments of an unknown distribution. The algorithm does not work for all types of distributions or for even reasonably high-order quadrature. In this work, we investigate the use of the Chebyshev algorithm and show that it is more robust than the P-D algorithm and can be used for a wider class of problems. The algorithm can also be used in a number of applications, where accurate computations of weighted integrals are required. We also illustrate the use of QMOM with the Chebyshev algorithm to solve several problems in aerosol science that could not be solved using the P-D algorithm.

► We suggest an improved algorithm to be used with the quadrature method of moments.
► The Chebyshev algorithm is used to compute the Gaussian quadrature formula.
► We demonstrate several advantages over the product-difference (P-D) algorithm.
► The new algorithm works with symmetric distributions and higher order quadrature.
► We consider applications in moment methods and Gaussian integration.