In this project, I review various numerical schemes that produce differential equations whose dynamics remains unchanged from the underlying continuous equations. They are used to transform the initially continuous problem which has an infinite number of degrees of freedom into a discrete problem where the degree of freedom is inevitably limited.
The sub-topics discussed are:
- Stability of Lotka-Volterra Differential Equations
- Classical Discretization
- Leslie Predator-prey Model
- Other Nonstandard Numerical Schemes
- Kolmogorov Model of Cooperative Systems