/ 95 08 24 6 v 1 6 A ug 1 99 5 SAGA - HE - 81 - 95 August 4 , 1995 Numerical solution of Q 2 evolution equations in a brute - force method

We investigate numerical solution of Q 2 evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method. Spin-independent flavor-nonsinglet and singlet equations with next-to-leading-order α s corrections are studied. Dividing the variables x and Q 2 into small steps, we simply solve the integrodifferential equations. Numerical results indicate that accuracy is better than 2% in the region 10 −4 < x < 0.8 if more than two-hundred Q 2 steps and more than one-thousand x steps are taken. The numerical solution is discussed in detail, and evolution results are compared with Q 2 dependent data in CDHSW, SLAC, BCDMS, EMC, NMC, Fermilab-E665, ZEUS, and H1 experiments. We provide a FORTRAN program for Q 2 evolution (and " devolution ") of nonsinglet-quark, singlet-quark, q i + ¯ q i , and gluon distributions (and corresponding structure functions) in the nucleon and in nuclei. This is a very useful program for studying spin-independent structure functions. No. of lines in distributed program, including test data, etc.: 2439 Nature of physical problem This program solves Altarelli-Parisi equations or modified evolution equations (Mueller-Qiu) with or without next-to-leading-order α s effects for a spin-independent structure function or quark distribution. Both flavor-nonsinglet and singlet cases are provided, so that the distributions, + i in the nucleon and in nuclei can be evolved. Method of solution We divide the variable x (and Q 2) into very small steps, and integration and differentiation are defined by df (x) dx = [f (x m+1) − f (x m)] ∆x m and dxf (x) = Nx m=1 ∆x m f (x m). Then, the integrodifferential equations are simply solved step by step, and this method is so called brute-force method. If the step numbers are increased, accurate results should be obtained. Restrictions of the program This program is used for calculating Q 2 evolution of a spin-independent flavor-nonsinglet-quark, singlet-quark, q + i , and gluon distributions (and corresponding structure functions) in the leading order or in the next-to-leading-order of α s. Q 2 evolution equations are the Altarelli-Parisi equations and the modified ones (Mueller-Qiu). The double precision arithmetic is used. The renormalization scheme is the modified minimal subtraction scheme (MS). A user provides the initial structure function or quark distribution as a subroutine or as a data file. Examples are explained in sections 4.2 and 4.3. Then, the user …