Before revision:   The obtained results not only resolve the contradiction between the dynamic consistency and high-order accuracy of NSFD schemes but also improve  some well-known results that have been published recently in [Applied Mathematics Letters 112(2021) 106775], [AIP Conference Proceedings 2302(2020) 110003] and [Applied Mathematics Letters 50(2015) 78-82]  ]  .
After revision:  The obtained results not only resolve the contradiction between the dynamic consistency and high-order accuracy of NSFD schemes but also improve some well-known results that have been published recently in [Applied Mathematics Letters 112(2021) 106775], [AIP Conference Proceedings 2302(2020) 110003] and [Applied Mathematics Letters 50(2015) 78-82] . Furthermore, as a simple but important application, we apply the constructed NSFD method for solving the logistic, sine, cubic, and Monod equations; consequently, the NSFD schemes constructed in the earlier work ] .