Habibullin, I.Zheltukhina, N.2018-04-122018-04-1220160402-9251http://hdl.handle.net/11693/36606The problem of constructing semi-discrete integrable analogues of the Liouville type integrable PDE is discussed. We call the semi-discrete equation a discretization of the Liouville type PDE if these two equations have a common integral. For the Liouville type integrable equations from the well-known Goursat list for which the integrals of minimal order are of the order less than or equal to two we presented a list of corresponding semi-discrete versions. The list contains new examples of non-autonomous Darboux integrable chains. © 2016 the authors.EnglishDarboux integrabilitydiscretizationn-integralcontinuum limitSemi-discrete chainx-integral35Q5137K60Article10.1080/14029251.2016.12481591776-0852