Introduction to nonstandard finite difference methods

In general, a given linear or nonlinear differential equation does not have a complete solution that can be expressed in a finite number of elementary functions. A first approach to decant this situation is to look for numerical integration techniques that can provide a precise solution to the differential equations. But, most numerical models do not preserve the properties of continuous equations. Seeking numerical schemes that preserve the qualitative properties of continuous equations remains a widespread problem in numerical analysis. The main objective of this seminar is to introduce the methodology of non-standard finite difference schemes that have already proved their effectiveness.