Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions

Temporal second- and high-order efficient one-step schemes are proposed for the damped nonlinear Schrödinger equation in high dimensions by combining the integrating factor method with the discretization matrices in diagonalized forms. Our schemes decouple the nonlinear part at tn+1 from the linear part and also have a compact representation, so they greatly save computational cost and storage. Numerical results are reported to exhibit the effectiveness and accuracy of the proposed schemes.