Numerical Solution of Altarelli-Parisi Equations

Abstract

We discuss numerical solution of Altarelli-Parisi equations in a Laguerre-polynomial method and in a brute-force method. In the Laguerre method, we get good accuracy by taking about twenty Laguerre polynomials in the flavor-nonsinglet case. Excellent evolution results are obtained in the singlet case by taking only ten Laguerre polynomials. The accuracy becomes slightly worse in the small and large $x$ regions, especially in the nonsinglet case. These problems could be implemented by using the brute-force method; however, running CPU time could be significantly longer than the one in the Laguerre method.