摘要：A mass conserved time-splitting difference method is presented for the one-dimensional dipolar Bose-Einstein condensates (BECs) described by a nonlocal nonlinear Schrödinger equation with a convolution term. As a result of the singularity in the convolution term, it brings difficulties both in mathematical analysis and in numerical simulations. By properly using the difference scheme to deal with the convolution term, an imaginary time method is given to compute the ground states and then a time-splitting method is obtained for dynamics of dipolar BECs. This time-splitting numerical method is mass conserved everywhere, and it has second-order accuracy and is also unconditionally stable. Numerical results are given to verify the stability and energy conservation when there is no blow up. Mathematics Subject Classification (2010) 65M06; 35Q41.
