I have done a project for my math class where we analyze the linear systems. We have classified the first and second-order linear systems and give a general formula for an n-linear system. We have used algebra notation and we have encountered with the companion matrix power to the n problem.
The n-linear systems are used widely in finance for loans, interests, etc.
Spacecraft mission will become more common. There are relevant open projects such that Mars colonization and exploring missions outside the Solar System.
These missions require high accuracy calculations because the error propagates in time and would be able to modify the trajectory.
There are many ways to face this problem: analytical or numerical approaches.
The analytical approaches could only be used for simplified problems, and thus it is really restrictive.
The numerical approaches commonly used and include metaheuristics and nonlinear programming. I have used genetic algorithms to solve a basic problem which consists of optimizing trajectory to travel to Mars from the Earth.