Solving Non-Linear Boundary Problems: Challenges and Numerical Methods

[Karlisbad]

Let's suppose we have a Non-linear operator (supposing is self-adjoint and all that) so:

$$cos(y'')+(y')^{2}y+xy=g(x)$$ with the boundary conditions for some a and be real

y(a)=0 and y(a)+2y(b)=0 then the "superposition principle" can't be applied so how the hell do you solve it

By the way, does "Non-linear Fourier Analysis or Harmonic analysis2 exists??

 

[HallsofIvy]

There are very few non-linear equations that are solvable. Most techniques for non-linear equations are approximation methods.

No, there are no "Fourier" methods for non-linear equations since those are based on linearity.

 

[Clausius2]

There is a good book of Keller that is called the same as the headings of this thread. It goes all about the numerical methods for this kind of problems.

Good Luck.