Split-step modified cubic B-splines collocation methods for nonlinear Schrödinger equations with Dirichlet boundary conditions

The split-step modified cubic B-splines collocation (SSM3BC) method is constructed by combining the split-step approach with the modified cubic B-splines collocation method for the two-dimensional (2D) nonlinear Schrodinger (NLS) equation. Numerical tests are carried out, and the SSM3BC schemes are efficient both for the one-dimensional (1D) and 2D NLS equations. It is also numerically verified that the proposed 1D and 2D schemes are second-order convergence both in time and space.