Abstract
In this paper and for the first time in the literature, we introduce a new three-stages symmetric six-step finite difference pair with optimal phase and stability properties. The basic characteristics of the new finite difference pair are: For this new finite difference pair we present a detailed analysis which consists of the following: The theoretical and numerical analysis of the produced new three-stages symmetric six-step finite difference pair, which are presented in this paper, show the effectiveness of the new scheme compared with other known or recently developed algorithms of the literature.
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