New Publication on second-order Nonstandard Finite Difference (NSFD) Method
Prof. Dr. Matthias Erhardt is pleased to share that his new article has been published in Applied Mathematics and Computation: M. T. Hoang and M. Ehrhardt, "A generalized second-order positivity-preserving numerical method for non-autonomous dynamical systems with applications", Appl. Math. Comput. 524 (September 2026), 130029.
In this paper, we develop a generalized second-order nonstandard finite difference (NSFD) method for nonautonomous dynamical systems governed by ODEs.
- Combines the NSFD framework with a new non-local approximation of the right-hand side
- Achieves second-order convergence
- Unconditionally preserves positivity of solutions for all step sizes
- Relaxes a common restrictive assumption in the literature (no need to require that the right-hand side does not vanish at time steps)
- Simple to implement and computationally efficient
This work contributes to the ongoing development of structure-preserving numerical methods for dynamical systems, especially where qualitative properties such as positivity are essential.
