标题： Q²演化方程的数值解比较 显示英文标题

标题： Comparison of numerical solutions for Q^2 evolution equations

摘要： Q^2演化方程不仅对于描述加速器实验中的强子反应非常重要，而且对于研究超高能宇宙射线也具有重要意义。 标准的方程称为DGLAP演化方程，它们是积分微分方程。 有求解部分子分布和碎裂函数的Q^2演化方程的方法。 由于这些方程无法解析求解，已经开发出各种方法用于数值求解。 我们特别通过关注数值精度和计算效率来比较暴力求解、拉盖尔多项式和梅林变换方法。 一种高效的解决方案可以用于例如对超高能宇宙射线的自上而下情景的研究。 显示英文摘要

摘要： Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q^2 evolution equations for parton-distribution and fragmentation functions. Because the equations cannot be solved analytically, various methods have been developed for the numerical solution. We compare brute-force, Laguerre-polynomial, and Mellin-transformation methods particularly by focusing on the numerical accuracy and computational efficiency. An efficient solution could be used, for example, in the studies of a top-down scenario for the ultrahigh-energy cosmic rays.