Local energy-preserving algorithms for nonlinear fourth-order Schrödinger equation with trapped term

Based on the rule that numerical algorithms should preserve the intrinsic properties of the original problem as many as possible, we propose two local energy-preserving algorithms for the nonlinear fourth-order Schrödinger equation with a trapped term. The local energy conservation law is preserved on any local time-space region. With appropriate boundary conditions, the first algorithm will be both globally charge- and energy-preserving and the second one will be energy-preserving. Numerical experiments show that the proposed algorithms provide more accurate solution than many existing methods and also exhibit excellent performance in preserving conservation laws.