A universal preprocessing algorithm of average kernel method with Gauss-Laguerre quadrature for double integrals

Abstract

To address the computational challenges posed by nonlinear collision kernels in the Smoluchowski equation, this study proposes a universal preprocessing algorithm for the average kernel method based on the Gauss-Laguerre quadrature for double integrals. With this algorithm, the numerical code accurately and efficiently determines the pre-exponential factor of the average kernel. Additionally, the exact pre-exponential factors of the four fundamental average kernels and their associated truncation error estimations were analyzed. The results demonstrate the reasonability and reliability of the preprocessing algorithm.