A new two-step finite difference pair with optimal properties

Abstract

A new four-stages symmetric two-step finite difference pair with optimal error, phase-lag and general stability properties is obtained, for the first time in the literature, in this paper. The new scheme has the following properties: For the new four-stages symmetric two-step finite difference pair we present a full theoretical analysis (error and stability analysis). The evaluation of the efficiency of the new developed four-stages symmetric two-step finite difference pair is based on its application on systems of coupled differential equations of the Schrodinger form.