A two-step high-order compact scheme for the Laplacian operator and its implementation in an explicit method for integrating the nonlinear Schrödinger equation

We describe and test an easy-to-implement two-step high-order compact (2SHOC) scheme for the Laplacian operator and its implementation into an explicit finite-difference scheme for simulating the nonlinear Schrödinger equation (NLSE). Our method relies on a compact ‘double-differencing’ which is shown to be computationally equivalent to standard fourth… CONTINUE READING