How can I use Newton’s Method when I have a 2D domain?

I have a 2D domain (x,y) and the implicit function I have to solve using the Newton's Method is:

alpha_test - dC/dx*tan(alpha_test) + dC/dy = 0

The input I have is the matrix domain (x,y), the values of C for each point of the domain.

I used the finite difference method to find dC/dx and dC/dy.

The output I need to obtain is a matrix with the values of alpha defined everywhere in my domain.

Thank you in advance for helping.

Answer 1

[John D'Errico]

Don't write code for Newton's method, when you can use fzero. Just put a loop around it, and call fzero for each pair of dC/dx and dC/dy.

Never write code to do what existing code already does well. This is certainly true unless you can write better code than the professional wrote, a person who is highly skilled in both MATLAB and in numerical analysis. (And if you can do that, then you would not be asking this question in the first palce.)