Padé and upwinding finite difference schemes for the quantum mechanical equation of motion

Abstract

AbstractA systematic approach is presented to search for a two‐level six‐point finite difference of Padé type for the numerical solution of the quantum mechanical equation of motion. A family of second order accurate Pade schemes is obtained and the stability properties are analysed by the von Neumann and matrix methods. Also, a similar stability analysis is also performed for a family of two‐level first order accurate upwinding difference schemes by the von Neumann and matrix methods. Discrepancies between the stability results obtained by the von Neumann and matrix methods are observed.