Abstract
A new five-stages symmetric two-step finite difference pair is developed, for the first time in the literature, in this paper. This new finite difference pair has optimal phase and stability properties The main characteristics of the new finite difference pair are: A full numerical analysis (error and stability analysis) is given for the new finite difference pair. The effectiveness of the new finite difference pair is evaluated by applying it on the approximate solution of systems of coupled differential equations of the Schrodinger form.
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