High order schemes for solving the time-dependent Schr\"odinger equation D. A. Volobueva1,2, A. A. Gusev 1,3,4, O. Chuluunbaatar,1,4,5, V. L. Derbov6, S. I. Vinitsky1,7, 1Joint Institute for Nuclear Research, Dubna, Russia; 2 Dubna branch of Lomonosov Moscow State University, Dubna, Russia; 3 Dubna State University, Dubna, Russia; 4Mongolian University of Science and Technology, Ulaanbaatar, Mongolia; 5 Institute of Mathematics and Digital Technology, Ulaanbaatar, Mongolia; 6Saratov State University, Saratov, Russia; 7 RUDN University, Moscow, Russia