# fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like

$$[A][X]=C\times\big(\exp([B][X])-1\big),$$

where $C$ is a constant and Both $[A]$ and $[B]$ are found out from two diff equations and boundary conditions.

Now my question is how am I able to find the value of $[X]$, I am thinking using fixed point method, but this is in matrix form, could any one give me any clue or hint?

• Do the square brackets denote a matrix? Fixed-point iteration method works similarly for matrix equations as it does for equations in one or more real unknowns. Newton's method works the same way too, but the derivative (or Jacobian) in it must be replaced with the Fréchet derivative (matrix derivative). – Kirill Jul 28 '15 at 3:50
• I think that the constant $C$ is not necessary. Also, I think that $[X]$ is a fixed point of the equation, so you want to avoid guesses too close since it will give you the trivial solution. – nicoguaro Jul 30 '15 at 3:39