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

Kejun Pan; Mingliang Xie

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arXiv · 2502.13378

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

Kejun Pan·Mingliang Xie

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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.

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Kejun Pan, Mingliang Xie. 2025-02-19. A universal preprocessing algorithm of average kernel method with Gauss-Laguerre quadrature for double integrals. https://arxiv.org/abs/2502.13378

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