The computation of average kernel with Gauss-Laguerre quadrature for double integrals

The use of average kernel method based on the Laplace transformation can significantly simplify the procedure for obtaining approximate analytical solution of Smoluchowski equation. However, this method also has its own shortcomings, one of which is the higher computational complexity of the binary Laplace transformation for a nonlinear collision kernel. In this study, a universal algorithm based on the Gauss-Laguerre quadrature for treating the double integral is developed to obtain easily and quickly pre-exponential factor of the average kernel. Furthermore, the corresponding truncation error estimate also provided.