Structurally Stable Numerical Schemes for Applied Dynamical Models

The paper deals with the construction of reliable numerical discretizations of continuous dynamical systems arising as models for different natural phenomena, with a focus on schemes which correctly replicate the properties of the original dynamical systems. The work is based on the new concept of topological dynamic consistency, which describes in precise terms the alignment; of the properties of the discrete dynamical system and the approximated continuous dynamical system. The derivation of structurally stable numerical schemes via, the nonstandard finite difference method is also demonstrated.