Method of characteristics and solution of DGLAP evolution equation in leading order (LO) and next to leading order (NLO) at small-x

In this paper the singlet and non-singlet structure functions have been obtained by solving Dokshitzer, Gribove, Lipatov, Alterelli, Parisi (DGLAP) evolution equations in leading order (LO) and next to leading order (NLO) at the small x limit. Here we have used a Taylor Series expansion and then the method of characteristics to solve the evolution equations. We have also calculated t and x-evolutions of deuteron structure function and the results are compared with the New Muon Collaboration (NMC) data.