I'm trying to learn myself more about non-linear differential equations and how I can use them in modeling of complex systems. However, I'm struggling in finding the correct "subject" name of this field of mathematics.
I am wondering if there is a common name for a subject regarding solving systems of non-linear differential equations. I have already been through linear algebra, however, If I understand correctly. This can't be applied to non-linear equations.
An example of what I want to model:
The control system of a spacecraft traveling through multiple atmospheric conditions which are all modeled with non-linear equations, which each of these depend on different parts of information about the spacecrafts speed, mass, surface etc.
So simply, what branch of mathematics is this? and what kind of mathematics category books should I look for?
There are several fields dealing with this subject:
Finding the differential equations that describe a problem would be the subject of mathematical modelling but also of a more applied discipline, such as physics or engineering in your example.
Most interesting non-linear differential equations cannot be solved analytically. Numerical analysis addresses the question of how to find numerical solutions to these equations with given initial conditions.
Understanding how the solutions to differential equations behave in general, how they change upon parameter changes, and so on would be the subject of the theory of dynamical systems. While this technically includes linear dynamical systems, they are well understood and boring from this field’s point of view.
Finally, how to make a dynamical system that you can steer behave in a certain way (such as your rocket) sounds like control theory to be, but I am no expert on this.