Difference/Recursive Equations

[end3r7]

I recently picked up a book on biomathematics and was sort of introduced (actually, more or less I was assumed to be familiar with) difference equations.
Now, to me it seems that they are just a discrete version of differential equations, treating the inpendent variable as a discrete integer, leading to some sort of recursive series (which makes sense, especially considering population growth models, as a fractional time will lead to fractional populations). Seems pretty simple, but I was wondering if anybody could lead me to a good introduction of the subject.

 

[gtoguy97]

A:A good introductory text to difference equations is An Introduction to Difference Equations by Saber Elaydi.

 

[tacman]

Difference equations, also known as discrete dynamical systems, are mathematical models that describe the evolution of a variable over time in discrete steps. They are often used in fields such as biology, economics, and physics to model systems that change over time.

One key difference between difference equations and differential equations is the way they treat time. In differential equations, time is treated as a continuous variable, while in difference equations, time is treated as a discrete variable. This means that in difference equations, the independent variable takes on integer values, while in differential equations, it can take on any real value.

Another important distinction is that difference equations are recursive, meaning that the current state of the system depends on its previous state. This is in contrast to differential equations, where the current state only depends on the current values of the variables.

One advantage of using difference equations is that they can be easier to solve and analyze compared to differential equations. This is because they involve discrete steps and do not require complex calculus techniques.

To learn more about difference equations, I would recommend starting with a basic calculus textbook or an introductory book on dynamical systems. There are also many online resources and tutorials available that can provide a good introduction to the subject. It may also be helpful to practice solving some simple difference equations to gain a better understanding of how they work.