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

TL;DR

This paper introduces a universal preprocessing algorithm utilizing Gauss-Laguerre quadrature to efficiently compute double integrals in the average kernel method, improving accuracy and reliability for nonlinear collision kernels in the Smoluchowski equation.

Contribution

It presents a novel preprocessing algorithm based on Gauss-Laguerre quadrature for the average kernel method, enabling precise and efficient computation of the pre-exponential factor.

Findings

Accurately determines the pre-exponential factor of the average kernel.

Analyzes the exact pre-exponential factors and truncation errors of fundamental kernels.

Demonstrates the algorithm's reasonability and reliability.

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.