DGLAP evolution at N³LO: exploring solutions with the Candia algorithm

We present the generalization to next-to-next-to-next-to-leading order (N³LO) in the strong coupling of Quantum Chromodynamics (QCD) of the Candia algorithm to solve the DGLAP evolution equations for unpolarized parton densities in the nucleon directly in the x-space. The algorithm is based on logarithmic expansions and can in principle be extended to all orders in QCD. An exact expansion equivalent to the exact solution of the DGLAP equation at N³LO is presented for the non-singlet sector.