A Padé compact high-order finite volume scheme for nonlinear Schrödinger equations

Abstract

In this work, a Padé compact high-order finite volume scheme is presented for the solution of one-dimensional nonlinear Schrödinger equations. The compact high-order finite volume schemes posses inherent conservation of the equations and high order accuracy within small stencils. Fourier error analysis demonstrates that the spectral resolution of the Padé compact finite volume scheme exceeds that of the standard finite volume schemes in terms of the same order of accuracy. Besides, the linear stability of the temporal discretization scheme is also performed by using the Fourier analysis. Numerical results are obtained for the nonlinear Schrödinger equations with various initial and boundary conditions, which manifests high accuracy and validity of the Padé compact finite volume scheme.