A Novel Second-Order Nonstandard Finite Difference Method for Solving One-Dimensional Autonomous Dynamical Systems

In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced analyzed. This based on non-local approximations for right-hand side functions differential equations in combination with denominator functions. The obtained results not only resolve contradiction between dynamic consistency high-order accuracy NSFD methods but also improve extend some well-known have been published recently [Applied Mathematics Letters 112(2021) 106775], [AIP Conference Proceedings 2302(2020) 110003] 50(2015) 78-82]. Furthermore, as simple important application, we apply constructed solving logistic, sine, cubic, Monod equations; consequently, schemes earlier work [Journal Computational Applied 110(1999) 181-185] are improved significantly. Finally, report numerical experiments to support illustrate theoretical assertions well advantages method.