The 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 a Taylor Series expansion has been used and then the method of characteristics has been used 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) and E665 data.