Nonstandard multistep multistage methods are constructed by replacing the timestep with a bounded function, achieving the same convergence order as standard methods while preserving qualitative properties for all positive step sizes.
Contributions to the mathematics of the nonstandard finite difference method and applications
2 Pith papers cite this work, alongside 247 external citations. Polarity classification is still indexing.
2
Pith papers citing it
247
external citations · OpenAlex
years
2026 2representative citing papers
Presents UFDSM based on cellular automata with a conservation nonstandard finite difference method that preserves positivity and fixed points, showing small discrepancies versus HEC-RAS in validation.
citing papers explorer
-
Some properties of high-order nonstandard multistep multistage methods
Nonstandard multistep multistage methods are constructed by replacing the timestep with a bounded function, achieving the same convergence order as standard methods while preserving qualitative properties for all positive step sizes.
-
A Novel Urban Flood Dynamical System Model and a Corresponding Nonstandard Finite Difference Method
Presents UFDSM based on cellular automata with a conservation nonstandard finite difference method that preserves positivity and fixed points, showing small discrepancies versus HEC-RAS in validation.